A terrific second-half performance by Aberdeen helped secure their passage to the fifth round of the Scottish Cup.
Motherwell had the better of the first half but failed to score and Rory Fallon's venomous strike at the start of the second period proved pivotal.
Craig Brown's side scored a quick second - Joe Shaughnessy tapping in a Jonny Hayes cross.
'Well caused a nervy last few seconds when Michael Higdon scored a penalty, but Aberdeen deservedly progressed.
It meant that for the second consecutive season they knocked Motherwell out of the competition at Fir Park, with a trip to Easter Road to play Hibernian their reward.
They began the match as they had the original tie - on the offensive.
Josh Magennis almost capitalised on slack defending by Shaun Hutchinson, his shot taking a nick off a Motherwell player on its way wide.
And from the resultant corner Fallon guided a header goalwards, but Darren Randolph comfortably plucked it out of the air.
Motherwell responded swiftly, though, and a fine move on the slippery surface resulted in a Stuart Carswell drive at goal, which Langfield did well to repel.
It quickly became apparent that Motherwell were adapting better to the slick conditions and Higdon should have added to his 11-goal tally for the season before a quarter of an hour had been played.
Stuart McCall's side mounted a rapid counter-attack down the right, with Chris Humphrey whipping a cross onto the striker's head, but he directed it just too high to trouble Langfield.
Aberdeen were trying to play a 3-4-3 formation, but in practice the wide midfielders - Magennis and Shaughnessy - were operating as additional defenders as Motherwell pushed Jamie Murphy and Humphrey forward in support of Higdon and Henrik Ojamaa.
But the visitors provided a reminder of their own threat just before the half-hour as Hayes rifled in an audacious drive from 25 yards, which Randolph managed to push over.
And the keeper was called into action again three minutes before the break. Clark Robertson did superbly to pull a cross back from the bye-line. It was met firmly by the head of Fallon but Randolph managed to turn it away to safety.
He was utterly helpless to prevent Fallon opening the scoring six minutes after the break though.
Hayes powered down the left and when his cross was only half-cleared, the New Zealander lashed a shot from just inside the box into Randolph's top-left corner.
Motherwell were denied an immediate equaliser by a terrific intervention from Mark Reynolds, who somehow prevented Higdon tapping in Stevie Hammell's cross.
But Aberdeen really had the bit between their teeth and though Shaughnessy sent a close-range shot wide and Randolph saved well from Niall McGinn and Gavin Rae, the second goal came as no surprise on 61 minutes.
Hayes again provided the cross from the left and Shaughnessy stole in at the back post for an easy finish.
Motherwell had completely lost the fluency that had been so evident in the opening period. By contrast, Aberdeen were knocking the ball about confidently, with Hayes looking especially lively.
With Aberdeen looking comfortable, they conceded an injury-time penalty when Robertson handled, allowing Higdon to beat Langfield from the spot, but the home side could not force an equaliser.