Motherwell and Aberdeen have it all to do again after two late goals led to stalemate and a replay at Fir Park on 11 December.
Aberdeen had the best of the match, without creating much in the way of clear-cut chances.
But Murphy let fly with a powerful shot from 25 yards with ten minutes to go to put the visitors ahead.
However, with full time looming, Niall McGinn rose to head home an equaliser which earned his side another chance.
Aberdeen have not beaten Motherwell at home since November 2008 and the Dons looked eager to end that poor run, with an early corner forced goalwards by Rory Fallon which stand-in keeper Lee Hollis leapt acrobatically to save.
Hollis endured an uncomfortable moment as he failed to judge the bounce of a Jonny Hayes drive from distance and the ball skiffed off his boot and bounced inches past the post.
Motherwell have been in good form on their travels however, and, after the Dons rearguard failed to clear a corner properly, Chris Humphrey forced Jamie Langfield to tip a thumping 20-yard drive over the bar.
Aberdeen were clearly targeting Hollis as a potential weak link, with Josh Magennis and Andrew Considine firing in long-range efforts which were comfortably held by the keeper.
Motherwell were struggling to create, but Jamie Murphy carved out a chance when he was teed up at the edge of the box following a mistake by Mark Reynolds, but his effort was steered wide.
The second half did not get off to as open a start, with misplaced passes and plenty of free-kicks conspiring to prevent any flowing play.
A dinked cross from Shaughnessy allowed Fallon the chance to flick a shot at the near post, but a deflection took it onto the post and out for a corner.
Motherwell were handed a chance from a set piece when Gavin Rae hauled down Keith Lasley 25 yards from goal.
Tom Hateley put plenty of curl on his effort, but Langfield watched it comfortably sail over.
Despite enjoying plenty of possession, Aberdeen were being restricted to shots from distance, Scott Vernon forcing a 20-yard volley wide.
The Motherwell players claimed loudly for a penalty for a handball by Mark Reynolds as he jumped for a high cross, but referee Willie Collum was uninterested.
The visitors were coming more into the match as it became stretched and Murphy picked up the ball on the left, drifted infield and let fly with a rasping 20-yard drive into the top right corner of the net to send the small band of travelling fans into raptures.
Their joy was short-lived however, as McGinn rose to direct a Considine cross into the net to score his ninth goal of the season and earn his side a replay.
Full Time The final whistle is blown by the referee.
Assist by Andrew Considine.
89:37 Goal scored
Goal - Niall McGinn - Aberdeen 1 - 1 Motherwell Niall McGinn finds the back of the net with a headed goal from close in. Aberdeen 1-1 Motherwell.
Andrew Considine crosses the ball,
Substitution Russell Anderson goes off and Cameron Smith comes on.
A cross is delivered by Rory Fallon, save by Lee Hollis.
The ball is delivered by Niall McGinn, Joe Shaughnessy takes a shot. Lee Hollis makes a save.
Stevie Hammell concedes a free kick for a foul on Johnny Hayes. Free kick taken by Jamie Langfield.
Johnny Hayes challenges Chris Humphrey unfairly and gives away a free kick. Free kick taken by Tom Hateley.
79:21 Goal scored
Goal - Jamie Murphy - Aberdeen 0 - 1 Motherwell Goal scored by Jamie Murphy from just outside the box to the top right corner of the goal. Aberdeen 0-1 Motherwell.
Unfair challenge on Keith Lasley by Rory Fallon results in a free kick. Free kick taken by Nicky Law.
Centre by Stevie Hammell, save by Jamie Langfield. Tom Hateley takes the inswinging corner, clearance made by Rory Fallon.
Stevie Hammell challenges Rory Fallon unfairly and gives away a free kick. Johnny Hayes crosses the ball in from the free kick.
Keith Lasley sends in a cross, Russell Anderson manages to make a clearance.
The ball is crossed by Tom Hateley, Stevie Hammell has a drilled shot. Andrew Considine gets a block in. Corner taken right-footed by Tom Hateley from the right by-line, clearance made by Andrew Considine.
The ball is crossed by Tom Hateley, Henrik Ojamaa has a headed effort at goal, save by Jamie Langfield.
Tom Hateley takes a outswinging corner to the near post, Russell Anderson makes a clearance.
Stevie Hammell delivers the ball, clearance by Russell Anderson.
Scott Vernon takes a shot from 35 yards and missed to the left of the target.
The ball is sent over by Joe Shaughnessy, clearance by Adam Cummins.
Unfair challenge on Russell Anderson by Henrik Ojamaa results in a free kick. Jamie Langfield takes the direct free kick.
Free kick awarded for an unfair challenge on Keith Lasley by Gavin Rae. Tom Hateley shoots direct from the free kick.
Shot by Mark Reynolds. Blocked by Adam Cummins.
The ball is swung over by Russell Anderson, Adam Cummins manages to make a clearance.
Chris Humphrey delivers the ball, clearance made by Josh Magennis.
Johnny Hayes produces a cross, Tom Hateley makes a clearance.
Centre by Joe Shaughnessy, clearance by Fraser Kerr. Inswinging corner taken from the right by-line by Johnny Hayes.
Jamie Murphy sends in a cross, Gavin Rae makes a clearance.
Johnny Hayes produces a cross, Adam Cummins makes a clearance.
Foul by Henrik Ojamaa on Russell Anderson, free kick awarded. Russell Anderson restarts play with the free kick.
Henrik Ojamaa challenges Russell Anderson unfairly and gives away a free kick. Direct free kick taken by Jamie Langfield.
Niall McGinn produces a cross.
The ball is crossed by Nicky Law, Jamie Langfield makes a save.
The second half has started.
45:00 +0:09 Half time
Half Time The whistle is blown to end the first half.
Unfair challenge on Johnny Hayes by Stevie Hammell results in a free kick. Johnny Hayes fires a strike on goal direct from the free kick.
Henrik Ojamaa concedes a free kick for a foul on Russell Anderson. Free kick taken by Russell Anderson.
Stevie Hammell delivers the ball, Mark Reynolds makes a clearance.
Andrew Considine challenges Michael Higdon unfairly and gives away a free kick. Adam Cummins restarts play with the free kick.
Joe Shaughnessy delivers the ball, Stevie Hammell gets a block in.
Michael Higdon is penalised for handball and concedes a free kick. Direct free kick taken by Scott Vernon.
Stevie Hammell challenges Johnny Hayes unfairly and gives away a free kick. Jamie Langfield takes the direct free kick.
The assistant referee flags for offside against Niall McGinn. Lee Hollis restarts play with the free kick.
Jamie Murphy delivers the ball, clearance by Russell Anderson.
Tom Hateley takes a outswinging corner from the right by-line to the near post, Joe Shaughnessy makes a clearance.
Free kick awarded for an unfair challenge on Nicky Law by Gavin Rae. Free kick crossed by Tom Hateley.
The referee gives a free kick against Chris Humphrey for handball. Jamie Langfield takes the free kick.
Jamie Murphy has an effort at goal from just inside the box that misses to the right of the target.
Mark Reynolds challenges Michael Higdon unfairly and gives away a free kick. Free kick taken by Nicky Law.
Effort from the edge of the box by Johnny Hayes goes wide of the right-hand upright.
Josh Magennis has an effort at goal from just outside the area which goes wide of the left-hand post.
Gavin Rae fouled by Nicky Law, the ref awards a free kick. Johnny Hayes takes the free kick.
The ball is swung over by Johnny Hayes, Stevie Hammell makes a clearance.
Shot from 35 yards by Andrew Considine went wide of the right-hand upright.
Effort from 18 yards by Josh Magennis. Save by Lee Hollis.
Handball decision goes against Chris Humphrey. Indirect free kick taken by Johnny Hayes.
Andrew Considine gives away a free kick for an unfair challenge on Michael Higdon. Direct free kick taken by Nicky Law.
The ball is delivered by Niall McGinn, save by Lee Hollis.
Johnny Hayes produces a cross, Jamie Murphy makes a clearance.
Drilled right-footed shot by Chris Humphrey. Save by Jamie Langfield. Outswinging corner taken right-footed by Tom Hateley from the right by-line, clearance by Rory Fallon.
Corner taken by Tom Hateley from the left by-line to the near post, Rory Fallon manages to make a clearance.
Tom Hateley crosses the ball from the free kick right-footed from left wing, clearance made by Gavin Rae.
Booking Joe Shaughnessy is shown a yellow card.
Joe Shaughnessy gives away a free kick for an unfair challenge on Jamie Murphy.
Tom Hateley crosses the ball, clearance by Russell Anderson.
The ball is delivered by Chris Humphrey, Joe Shaughnessy makes a clearance.
Tom Hateley gives away a free kick for an unfair challenge on Rory Fallon. Johnny Hayes sends in a cross, Header from close range by Scott Vernon misses to the right of the goal.
Shot from 18 yards from Johnny Hayes. Lee Hollis makes a save. Outswinging corner taken left-footed by Johnny Hayes.
Niall McGinn has an effort at goal from outside the box which misses left.
The ball is crossed by Andrew Considine.
The ball is swung over by Scott Vernon, Fraser Kerr makes a clearance.
Corner taken by Johnny Hayes, clearance made by Fraser Kerr.
Keith Lasley produces a right-footed shot from the edge of the area and misses to the left of the target.
Josh Magennis is caught offside. Lee Hollis takes the free kick.
Tom Hateley sends in a cross, clearance by Andrew Considine.
The ball is swung over by Johnny Hayes, Rory Fallon takes a shot. Save made by Lee Hollis.
Johnny Hayes sends in a cross, Adam Cummins manages to make a clearance. Corner taken by Johnny Hayes played to the near post.
The match gets underway.
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