Kilmarnock had to work hard against 10-man East Fife to progress to the semi-finals of the Scottish League Cup.
An evenly-contested first half ended with Robert Ogleby being sent off after picking up a second yellow card.
Killie made the breakthrough on 73 minutes when Mohamadou Sissoko latched onto a spilled ball by Fifers goalkeeper Marc Ridgers.
The tie was over 10 minutes from time when Gary Harkins pounced on another loose ball to blast home from 14 yards.
East Fife had taken care of Dunfermline and Aberdeen earlier in the tournament and gave the hosts a few first-half scares, with Ogleby their main threat.
Kilmarnock dominated possession for long spells and leading scorer Paul Heffernan turned and shot wide after a well-worked early corner.
Ogleby then replied with two dangerous shots as he showed Killie skipper Manuel Pascali a clean pair of heels on both occasions.
Ridgers made comfortable saves from each of Killie's front three players - Harkins, Dean Shiels and Heffernan and home goalkeeper Anssi Jaakkola was called into action just before the interval to parry Robert Sloan's 30-yard free-kick before full-back Matthew Park blazed the rebound over.
But the visitors suffered a serious blow when Ogelby was sent off.
The Wales Under-21 striker had been booked for a reckless challenge on Danny Buijs and received his second yellow card when he caught Rory McKeown with a kick after the defender had dispossessed him.
Buijs fired just over as Killie stepped up the pressure against depleted opponents in the second half and Shiels was denied by a great last-ditch challenge from John Ovenstone, while Heffernan's 20-yard strike shaved the post.
But the 10 men were not consigned to defending and Sissoko to divert needed to divert a shot from Ryan Wallace over and David Whyte could not turn Jon Ovenstone's flick on target from close range from the resulting corner.
Kilmarnock substitute David Silva saw a long-range effort fizz over the crossbar before a goalkeeping error presented the hosts with the opening goal.
Ridgers, who saved three penalties in the shoot-out with Aberdeen, came for a corner but could not hold the ball amid a ruck of bodies and Sissoko fired into the top corner after controlling the loose ball.
The Scotland Under-21 squad member recovered to make a flying save from Shiels following a counter-attack as Kilmarnock looked to build on their lead.
Silva hit the post after an incisive move and Harkins doubled the advantage in the 80th minute when Ridgers could not keep out his angled drive after Heffernan's progress had been halted by a good tackle just inside the box.
Kilmarnock manager Kenny Shiels : "When I first came to the club, they told me it was the second biggest derby in Europe after Barcelona - Ayr against Kilmarnock.
"It's mouth-watering prospect that one, I'm told, because there is an intensity there.
"Even the little villages outside Kilmarnock, I'm told some are all Ayr United and some villages are all Kilmarnock supporters.
"I don't really have a view because you have to respect the other teams, but Kilmarnock and Ayr would be a good draw.
"I'm delighted for my chairman and the club.
"To be in the semi-finals of the cup and one point off the top six, I think is a fantastic start for the club when you consider we've had to rebuild a team within a short period of time.
"I'm pleased to get to the semis because it was nervy out there at times."
East Fife manager John Robertson : "I'm disappointed for the players and the fans because I genuinely believe, if it had stayed 11 against 11, we could have been sitting in the semi-finals of the Cup.
"We felt really disappointed to come in level at half-time - and a man down. They played some lovely football, but they didn't hurt us.
"When you talk about cup upsets, you need to be at your best, which we were.
"You need to stop the opposition playing, which we did magnificently well. And you need that wee ounce of luck and I think that's the only thing that let us down."
Live Text Commentary
Full Time The referee ends the match.90:00 +1:38
James Dayton fouled by Craig Johnstone, the ref awards a free kick. The free kick is delivered left-footed by James Dayton from right wing.88:19
Inswinging corner taken by Craig Johnstone.87:39
Free kick awarded for a foul by James Dayton on Matthew Park. Ryan Wallace takes the free kick. Handball by Mohamadou Sissoko. Ryan Wallace delivers the ball from the free kick right-footed from left wing, Mohamadou Sissoko makes a clearance.86:57
Paul Heffernan produces a right-footed shot from the edge of the box and misses to the left of the goal.85:58
The ball is swung over by Dean Shiels. Mark Ridgers fouled by Paul Heffernan, the ref awards a free kick. Mark Ridgers restarts play with the free kick.85:22
Inswinging corner taken from the right by-line by James Dayton.84:43
The assistant referee flags for offside against David Silva. Free kick taken by Mark Ridgers.82:40 Substitution
Substitution (East Fife) makes a substitution, with Paul McQuade coming on for Darren Smith.82:26 Substitution
Substitution James Dayton joins the action as a substitute, replacing James Fowler.82:18
Effort on goal by Danny Buijs from a long way out goes over the bar.81:47
Inswinging corner taken right-footed by David Silva from the left by-line to the near post, clearance made by David Muir.80:09
Paul Heffernan provided the assist for the goal.80:09 Goal scored
Goal! - Gary Harkins - Kilmarnock 2 - 0 East Fife A goal is scored by Gary Harkins from inside the area to the bottom left corner of the goal. Kilmarnock 2-0 East Fife.79:35 Booking
Booking David White booked for dissent.79:19
David Silva produces a right-footed shot from deep inside the penalty area and hits the post.78:34
Alex Pursehouse produces a cross, clearance made by John Ovenstone.76:08
Dean Shiels takes a shot. Mark Ridgers makes a brilliant save.75:56
Ryan Wallace concedes a free kick for a foul on Danny Buijs. Alex Pursehouse takes the direct free kick.74:50
The ball is delivered by Alex Pursehouse.
Assist on the goal came from Garry Hay.72:37 Goal scored
Goal! - Mohamadou Sissoko - Kilmarnock 1 - 0 East Fife Mohamadou Sissoko scores a goal from inside the penalty area to the top right corner of the goal. Kilmarnock 1-0 East Fife.72:08
Garry Hay takes the inswinging corner,71:23
Corner taken by Garry Hay, David White manages to make a clearance.71:00
Garry Hay takes the inswinging corner, Dean Shiels sends in a cross, Craig Johnstone gets a block in.70:46
A cross is delivered by Alex Pursehouse, Paul Heffernan takes a shot. Blocked by David White.68:56
Ryan Wallace concedes a free kick for a foul on Mohamadou Sissoko. Alex Pursehouse takes the free kick.68:21
David Silva takes a long range shot clearing the bar.67:10
Ryan Wallace produces a right-footed shot from outside the penalty box and misses right.66:31
Shot from just outside the box by David Silva misses to the left of the goal.64:30
Garry Hay crosses the ball.63:20
Corner taken by Dean Shiels, Manuel Pascali takes a shot. Mark Ridgers makes a save.62:09
Effort on goal by Danny Buijs from just inside the penalty area goes harmlessly over the target.62:03
A cross is delivered by Garry Hay.61:11
Gary Harkins produces a header from deep inside the six-yard box which goes wide of the right-hand post.59:50
The ball is delivered by Garry Hay, free kick awarded for an unfair challenge on Matthew Park by Gary Harkins. Mark Ridgers takes the free kick.58:33 Substitution
Substitution David Silva comes on in place of Liam Kelly.58:05
Danny Buijs has an effort at goal from just outside the box which goes wide of the left-hand post.57:05
Gary Harkins challenges David White unfairly and gives away a free kick. Free kick taken by David White.55:46
Gary Harkins produces a header from close range which goes wide of the left-hand upright.53:52 Substitution
Substitution Robert Sloan leaves the field to be replaced by Craig Johnstone.53:27
Garry Hay produces a cross, Robert Sloan manages to make a clearance.52:02
Ryan Wallace takes a shot. Manuel Pascali gets a block in. Robert Sloan takes a inswinging corner from the right by-line played to the near post, Effort on goal by John Ovenstone from deep inside the penalty area misses to the right of the target.51:18
Paul Heffernan produces a right-footed shot from the edge of the box and misses to the left of the goal.50:02
The ball is sent over by Alex Pursehouse.48:42
Outswinging corner taken by Dean Shiels, clearance made by John Ovenstone.47:48
Corner taken by Dean Shiels from the left by-line, fantastic save by Mark Ridgers.47:44
Garry Hay produces a cross, Robert Linn manages to make a clearance.45:58
Danny Buijs produces a right-footed shot from inside the area that goes over the bar.45:13
The ball is sent over by Garry Hay, Scott Durie manages to make a clearance. Short corner worked by Dean Shiels.45:01
The second half kicks off.45:01 Substitution
Substitution Rory McKeown leaves the field to be replaced by Garry Hay.45:00 +2:41 Half time
Half Time The players leave the pitch at half time.45:00 +2:31
Alex Pursehouse delivers the ball, save by Mark Ridgers.45:00 +0:32
Manuel Pascali takes the free kick.45:00 +0:32 Dismissal
Dismissal The referee shows Robert Ogleby a red card for second bookable offence.45:00 +0:26
Robert Ogleby concedes a free kick for a foul on Rory McKeown.42:35
Danny Buijs concedes a free kick for a foul on Robert Linn. Free kick taken by Mark Ridgers.42:02
Shot by Liam Kelly missed to the left of the net.41:31
Scott Durie gives away a free kick for an unfair challenge on Rory McKeown. Dean Shiels restarts play with the free kick.40:08
Robert Sloan has a direct shot on goal from the free kick, save by Anssi Jaakkola. Shot from close in by Matthew Park misses to the left of the goal.40:08 Booking
Booking The referee books Alex Pursehouse for not retreating ten yards at a set play.39:00
Free kick awarded for a foul by Manuel Pascali on Robert Ogleby.38:23
Gary Harkins produces a cross, save by Mark Ridgers.37:58
Inswinging corner taken right-footed by Dean Shiels from the left by-line, clearance made by David White.37:09
James Fowler produces a cross.36:26
Dean Shiels has an effort at goal from deep inside the area missing to the left of the target.33:41
Liam Kelly takes a shot. David White gets a block in.33:14
Robert Ogleby is caught offside. Mohamadou Sissoko restarts play with the free kick.32:07
Corner taken right-footed by Dean Shiels to the near post, clearance by Robert Sloan.30:21
Corner taken right-footed by Dean Shiels, Headed effort from deep inside the area by Manuel Pascali misses to the left of the goal.29:16
Rory McKeown takes a shot.28:35
Paul Heffernan takes a shot. Save made by Mark Ridgers.27:47
The ball is crossed by Scott Durie.26:37
Dean Shiels takes a shot. Comfortable save by Mark Ridgers.25:11
Dean Shiels takes the inswinging corner, clearance made by David Muir.24:38
Robert Ogleby is flagged offside by the assistant referee. Anssi Jaakkola restarts play with the free kick.22:51
Ryan Wallace takes a shot. Manuel Pascali gets a block in.22:33
Rory McKeown crosses the ball, Scott Durie manages to make a clearance.21:44
A cross is delivered by Alex Pursehouse, save made by Mark Ridgers.20:56
Robert Ogleby produces a right-footed shot from the edge of the box and misses to the right of the goal.20:27
Paul Heffernan gives away a free kick for an unfair challenge on John Ovenstone. Mark Ridgers takes the free kick.19:38 Booking
Booking Robert Ogleby is cautioned by the ref for unsporting behaviour.17:46
Shot by Paul Heffernan from deep inside the penalty area misses to the left of the goal.14:05
Robert Ogleby produces a right-footed shot from the edge of the box and misses to the right of the goal.11:51
Free kick awarded for an unfair challenge on John Ovenstone by Paul Heffernan. Mark Ridgers takes the direct free kick.10:42
Paul Heffernan is caught offside. Free kick taken by Mark Ridgers.9:55
Outswinging corner taken right-footed by Dean Shiels from the right by-line, Darren Smith manages to make a clearance.8:46
Short corner taken by Dean Shiels from the left by-line, Paul Heffernan produces a right-footed shot from deep inside the penalty area which goes wide of the left-hand post.8:30
Gary Harkins takes a shot. Save by Mark Ridgers.4:26
Robert Sloan takes the inswinging corner, clearance made by Gary Harkins.2:05
Shot by Liam Kelly from a long way out goes over the target.1:47
Free kick awarded for a foul by David Muir on Alex Pursehouse. Alex Pursehouse takes the free kick.1:21
Unfair challenge on Liam Kelly by Darren Smith results in a free kick. Manuel Pascali takes the free kick.0:00
The referee gets the match started.
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