Celtic will face Kilmarnock in the Scottish Communities League Cup final after overcoming Falkirk at Hampden.
Scott Brown's penalty gave Celtic a 27th-minute advantage.
But Jay Fulton, son of former Celtic and Falkirk midfielder Steve, levelled five minutes before half-time with a composed finish.
Anthony Stokes restored Celtic's lead with an excellent free-kick on 56 minutes and the striker got his second with a tap-in late on.
With the Bairns having knocked Rangers and Dundee United out of the competition in an earlier round, the First Division side were hoping to claim a third Scottish Premier League scalp, while Celtic were looking to continue their push for the domestic treble.
Falkirk's top goalscorer Farid El Alagui was unable to test Celtic goalkeeper Fraser Forster with a first-time shot that flew wide early on.
Celtic began to assert themselves and Brown's well-struck shot was touched onto the post by Michael McGovern.
Gary Hooper converted the rebound only to have his celebrations cut short by the offside flag but television replays suggested the goal should have stood.
The frame of the Falkirk goal was struck again when Thomas Rogne's downward header from James Forrest's corner bounced up onto the bar.
Rogne's presence at a corner was the catalyst for the opening goal as Darren Dods was penalised for grappling with the Celtic defender in the box.
Brown confidently stroked the spot-kick to McGovern's left as the keeper dived in the other direction.
El Alagui's shot into the arms of Forster lacked power as Falkirk tried to respond quickly.
A slack pass from Victor Wanyama allowed the Bairns to mount the attack that would give them their equaliser.
David Weatherston retrieved, pushed down the left and cut the ball inside for Kallum Higginbotham.
Higginbotham had the awareness to spot Fulton's advancing run on the right-hand side of the penalty area and the inch-perfect pass was coolly converted by the 17-year-old.
Rogne was unable to connect with a teasing Brown free-kick and Forrest was denied by McGovern in the closing stages of the first half.
Steven Pressley marched onto the pitch just after the half-time whistle to remonstrate with referee Euan Norris and, as a result, the Falkirk manager watched the second half from the stand.
Fulton scooped the ball over after meeting Higginbotham's high, hanging cross shortly after play resumed.
Rogne was frustrated by the crossbar again with a deflected shot from Charlie Mulgrew's corner and, in the melee that followed, Stokes claimed unsuccessfully for a handball against Murray Wallace before the ball was cleared.
However, Celtic quickly won a free-kick and Stokes superbly curled the ball home to register a goal against his former club.
Fulton's replacement Blair Alston fired wide from the edge of the box before Forster made a double save to deny Dods and Stewart Murdoch as Falkirk continued to threaten.
At the other end, Joe Ledley's effort was deflected wide by Kieran Duffie and McGovern held a curving Mulgrew free-kick.
But Celtic did get a third goal on 86 minutes when Hooper burst towards the bye-line and cut back for Stokes to apply a simple finish.
Neil Lennon's side will return to the national stadium to face Killie on 18 March, the latter having beaten Ayr United in Saturday's first semi-final .
Live Text Commentary
Full Time The referee blows for the end of the match.90:00 +4:00
Charlie Mulgrew concedes a free kick for a foul on Mark Millar. Direct free kick taken by Mark Millar.90:00 +2:31 Substitution
Substitution Craig Sibbald replaces Kallum Higginbotham.90:00 +0:41
Farid El Alagui gives away a free kick for an unfair challenge on Charlie Mulgrew. Scott Brown takes the direct free kick.89:46
Outswinging corner taken right-footed by Mark Millar from the right by-line.88:48
Effort on goal by Kris Commons from just inside the penalty box goes harmlessly over the target.86:40 Substitution
Substitution Anthony Stokes goes off and Kris Commons comes on.86:10 Substitution
Substitution Jordan White on for David Weatherston.85:21
Assist by Gary Hooper.85:21 Goal scored
Goal! - Anthony Stokes - Falkirk 1 - 3 Celtic A goal is scored by Anthony Stokes from inside the six-yard box low into the middle of the goal. Falkirk 1-3 Celtic.85:12
Centre by Gary Hooper,82:03
Blair Alston gives away a free kick for an unfair challenge on James Forrest. Charlie Mulgrew shoots direct from the free kick, save by Michael McGovern.79:20
Sung-Yeung Ki takes the inswinging corner, Thomas Scobbie makes a clearance.78:15
Drilled left-footed shot by Stewart Murdoch. Save by Fraser Forster.77:58
Darren Dods has a drilled shot. Fraser Forster makes a fantastic save.77:29
Corner taken by Mark Millar.76:08
Free kick awarded for a foul by Victor Wanyama on Kallum Higginbotham. Mark Millar crosses the ball from the free kick right-footed from right wing, clearance made by Charlie Mulgrew.70:45
Effort on goal by Gary Hooper from 18 yards. Blocked by Murray Wallace.70:26
The ball is swung over by Charlie Mulgrew, clearance by Murray Wallace.69:01
Outswinging corner taken right-footed by Mark Millar from the right by-line, Charlie Mulgrew makes a clearance.
Substitution (Celtic) makes a substitution, with Adam Matthews coming on for Du-Ri Cha.66:42
Kallum Higginbotham crosses the ball, clearance made by Scott Brown.65:15
Effort from inside the area by Blair Alston misses to the left of the target.63:38
Sung-Yeung Ki takes the inswinging corner, Murray Wallace makes a clearance.63:00
Foul by David Weatherston on Du-Ri Cha, free kick awarded. Charlie Mulgrew delivers the ball from the free kick left-footed from right wing, clearance made by Darren Dods.60:51 Substitution
Substitution (Falkirk) makes a substitution, with Blair Alston coming on for Jay Fulton.59:04
Sung-Yeung Ki takes a shot from 30 yards. Michael McGovern makes a comfortable save.58:02
Joe Ledley concedes a free kick for a foul on Jay Fulton. Mark Millar takes the free kick.56:51
Free kick taken by Scott Brown.56:51 Booking
Booking Mark Millar goes into the book for unsporting behaviour.56:37
Mark Millar concedes a free kick for a foul on Sung-Yeung Ki.55:23
The assist for the goal came from Victor Wanyama.55:23 Goal scored
Goal! - Anthony Stokes - Falkirk 1 - 2 Celtic Free kick scored by Anthony Stokes from outside the box to the bottom left corner of the goal. Falkirk 1-2 Celtic.55:02
Free kick awarded for an unfair challenge on Victor Wanyama by Farid El Alagui.53:41
Corner taken left-footed by Charlie Mulgrew, Thomas Rogne has an effort at goal.50:22
Kallum Higginbotham sends in a cross, Close range effort by Jay Fulton clears the crossbar.49:46
Joe Ledley challenges Jay Fulton unfairly and gives away a free kick. Michael McGovern takes the direct free kick.48:18
Foul by Scott Brown on Stewart Murdoch, free kick awarded. Murray Wallace restarts play with the free kick.46:22
Unfair challenge on Victor Wanyama by Mark Millar results in a free kick. Direct free kick taken by Charlie Mulgrew.45:01
The referee starts the second half.45:01 Substitution
Substitution (Celtic) makes a substitution, with Sung-Yeung Ki coming on for Emilio Izaguirre.45:00 +1:05 Half time
Half Time The referee calls an end to the first half.44:59
James Forrest takes a shot. Save made by Michael McGovern.43:58
Centre by Kallum Higginbotham, Scott Brown makes a clearance.42:46
Free kick awarded for a foul by Stewart Murdoch on Victor Wanyama. The ball is crossed by Scott Brown, Close range header by Thomas Rogne misses to the right of the target.40:50
The referee blows for offside. Indirect free kick taken by Fraser Forster.39:10
Assist on the goal came from Kallum Higginbotham.39:10 Goal scored
Goal! - Jay Fulton - Falkirk 1 - 1 Celtic Jay Fulton gets on the score sheet with a goal from inside the box low into the middle of the goal. Falkirk 1-1 Celtic.38:35
Anthony Stokes has a drilled shot. Darren Dods gets a block in.35:57
Farid El Alagui challenges Thomas Rogne unfairly and gives away a free kick. Scott Brown takes the direct free kick.34:57
Anthony Stokes is flagged offside by the assistant referee. Michael McGovern takes the indirect free kick.33:33
James Forrest sends in a cross, clearance by Darren Dods.33:05
Corner from left by-line taken by James Forrest.28:34
Emilio Izaguirre concedes a free kick for a foul on Farid El Alagui. Mark Millar takes the free kick.27:10
Farid El Alagui takes a shot. Save by Fraser Forster.26:10
The assist for the goal came from Thomas Rogne.26:10 Goal scored
Goal! - Scott Brown - Falkirk 0 - 1 Celtic Penalty taken right-footed by Scott Brown and scored. Falkirk 0-1 Celtic.25:42 Booking
Booking Booking for Darren Dods for unsporting behaviour.24:51
Corner taken by Charlie Mulgrew from the right by-line, Darren Dods challenges Thomas Rogne unfairly and gives away a Penalty.21:15
Free kick taken by Fraser Forster.21:15 Booking
Booking Stewart Murdoch booked.21:07
Unfair challenge on Scott Brown by Stewart Murdoch results in a free kick.20:51
The ball is crossed by Kallum Higginbotham.18:38
Unfair challenge on Thomas Rogne by Darren Dods results in a free kick. Fraser Forster takes the direct free kick.17:55
Corner taken by Mark Millar from the right by-line, Thomas Rogne manages to make a clearance.15:44
Corner taken by James Forrest, Header from close range by Thomas Rogne bounces off the post.14:44
Jay Fulton fouled by Emilio Izaguirre, the ref awards a free kick. Direct free kick taken by Kieran Duffie.10:54
The referee blows for offside against Gary Hooper. Michael McGovern restarts play with the free kick.10:39
Shot from 20 yards by Scott Brown. Save by Michael McGovern.9:05
A cross is delivered by Emilio Izaguirre, clearance by Stewart Murdoch.7:17
Farid El Alagui produces a left-footed shot from the edge of the area and misses to the left of the goal.6:33
Free kick awarded for a foul by Victor Wanyama on Kallum Higginbotham. Thomas Scobbie takes the direct free kick.5:08
Charlie Mulgrew takes the outswinging corner, clearance by Stewart Murdoch.4:07
Free kick awarded for a foul by Murray Wallace on Charlie Mulgrew. Fraser Forster takes the direct free kick.3:02
Effort from just outside the area by Kieran Duffie goes over the target.1:10
Farid El Alagui challenges Thomas Rogne unfairly and gives away a free kick. Direct free kick taken by Du-Ri Cha.0:00
The match has kicked off.
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