John Sutton set the tone for an entertaining tie on Sunday when he headed home in the first minute but David Goodwillie stunned the visitors with an acrobatic effort just before the break.
Motherwell had barely stopped celebrating Sutton's second when substitute John Daly forced a replay in the 73rd minute.
Another match is the last thing United manager Peter Houston would have wanted before the game amid their heavy fixture schedule but Motherwell came closer to averting the need for the March 29 replay at Fir Park in the closing stages.
Houston brought back Craig Conway, Paul Dixon, Prince Buaben and Danny Swanson after picking his team for Thursday's victory over Hamilton with the cup tie in mind.
Daly was on the bench again after netting an injury-time winner against the Accies on his return from hernia surgery, while Motherwell recalled Stephen Craigan and Steven Saunders with Steve Jennings missing through suspension.
The visitors netted after 50 seconds when Stevie Hammell, who was playing in left midfield, swung a corner towards the back post and Sutton timed his jump perfectly to head down and into the net from six yards.
Swanson saw a free-kick comfortably held by Darren Randolph as United pushed midfielders forward but Motherwell were finding room on the break with Francis Jeffers setting up Jamie Murphy for a weak long-range shot before curling wide himself.
Randolph pulled off a brilliant save in the 18th minute, getting down well to stop Goodwillie's shot after the striker had shown good trickery inside the box following a weak header by Saunders.
The Motherwell goalkeeper made a more routine stop as Swanson and Conway carved out a good chance for Buaben, whose shot lacked conviction.
United goalkeeper Dusan Pernis pushed over Keith Lasley's powerful 20-yard strike and Swanson was booked for diving as United struggled to break the visitors down.
Buaben and Jeffers threatened from long range and United's frustration was evident when Dixon kicked out at Tom Hateley off the ball, with referee Calum Murray oblivious.
Motherwell had a let-off when Goodwillie went down under a risky penalty box challenge from Saunders, although the striker's exaggerated fall might have dissuaded Murray from awarding a spot-kick. Hateley, whose misplaced pass had put Motherwell under pressure, was booked for a foul on Swanson in the build-up.
But Goodwillie soon levelled in spectacular fashion in the 40th minute. Conway's right-wing cross went behind the forward but he produced a superb overhead kick to beat Shaun Hutchinson to the ball eight yards out.
The audacity of the effort appeared to take Randolph by surprise, with the Irishman's touch unable to stop it nestling in the corner.
But there was some controversy surrounding the goal, with Motherwell left-back Gavin Gunning claiming to have had his heels clipped by Conway before conceding possession.
Motherwell threatened first after an even start to the second half with Pernis pushing away Lasley's low strike after Jeffers had laid off the ball 20 yards out.
Daly came on for Conway as United prepared to take a 63rd-minute corner and immediately headed the delivery from Barry Douglas, but could not steer the ball on target.
Dixon turned Gunning's low cross just past his own goal after patient and incisive build-up play from the visitors down the left, more of which yielded Sutton's second goal.
Hammell played a one-two with Jeffers and sent in a low cross which Sutton converted from close range at the near post.
But United levelled after Swanson got to the byline on the right and lifted the ball across the face of goal.
The cross was too high for Goodwillie but Daly emerged unmarked at the back post and slotted home with his left foot from eight yards.
Craigan exchanged words with Houston and Goodwillie after the United striker returned possession to Motherwell following treatment to Gunning by kicking the ball out for a throw deep in Motherwell's half.
But the visitors, who knocked United out of the Co-operative Insurance Cup at Fir Park, came closest to having the final say on several occasions. Saunders was not far off from 30 yards and Hateley's cross flashed just in front of Jeffers before substitute Chris Humphrey volleyed wide from a tight angle.