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.