Johnny Russell's looping header sealed victory for Dundee United and moved them level on points with their opponents Motherwell.
Henrik Ojamaa was denied by the goal frame either side of half-time as Motherwell pressed hard for an opener.
Gavin Gunning had come close with a first-half free-kick for the visitors.
And, after claiming an injury-time draw against Celtic at the weekend, the Tangerines benefited from another late goal as Russell's header found the net.
The Steelmen went into the match knowing capturing all three points would take them up to third in the Scottish Premier League while United were seeking to join 'Well in sixth place.
With Celtic's Champions League match against Barcelona in nearby Glasgow being broadcast on television, a hearty band of 3,941 fans braved the damp conditions and were warmed by an exciting opening half.
Michael Higdon was left unmarked at the back post to tee up strike partner Jamie Murphy but United goalkeeper Radoslaw Cierzniak improvised well to keep the shot out.
The visitors responded and a breakaway from a Motherwell corner ended with Stuart Armstrong blazing over after latching on to Russell's disguised pass.
Dundee United then won a free-kick around 25 yards out and former Motherwell player Gunning stung the palms of Randolph before the keeper denied Armstrong in the aftermath.
Ojamaa had the home crowd on their feet when he burst down the left, cut inside and unleashed a powerful shot but both player and fans were left disappointed as the ball rebounded of the bar.
And the Estonian's agony continued when his low, angled drive clipped the base of the post on 56 minutes.
United came back into the match and Willo Flood's corner into a crowded six-yard area was diverted towards goal only to be cleared by Steven Hammell on the goal-line.
But Peter Houston's side grew in confidence and Keith Watson picked out Russell on the left-hand side of the box with six minutes to go and the striker nodded the ball over Randolph and into the net.
Motherwell went back on the attack but could not find a leveller, meaning they sustain a third straight home defeat.
Full Time The referee signals the end of the game.
Tom Hateley restarts play with the free kick.
90:00 +3:13 Booking
Booking Mark Millar goes into the book.
Mark Millar concedes a free kick for a foul on Nicky Law.
Gavin Gunning takes the free kick.
90:00 +2:16 Booking
Booking Adam Cummins goes into the referee's book.
Gary Mackay-Steven fouled by Adam Cummins, the ref awards a free kick.
Corner from the right by-line taken by Stevie Hammell, Brian McLean makes a clearance.
Foul by Stuart Armstrong on Tom Hateley, free kick awarded. Free kick taken by Tom Hateley.
Substitution Chris Humphrey goes off and Omar Daley comes on.
Substitution Mark Millar on for Johnny Russell.
The assist for the goal came from Keith Watson.
Assist on the goal came from Rudi Skacel.
83:21 Goal scored
Goal - Johnny Russell - Motherwell 0 - 1 Dundee U Johnny Russell scores a headed goal from deep inside the penalty area. Motherwell 0-1 Dundee Utd.
Effort on goal by Nicky Law from outside the area goes harmlessly over the bar.
Unfair challenge on Chris Humphrey by Gary Mackay-Steven results in a free kick. Tom Hateley restarts play with the free kick.
Handball decision goes against Brian McLean. Nicky Law restarts play with the free kick.
Substitution Rudi Skacel comes on in place of John Rankin.
Substitution Robert McHugh joins the action as a substitute, replacing Henrik Ojamaa.
Chris Humphrey produces a right-footed shot from deep inside the area which goes wide of the left-hand post.
Corner from left by-line taken by Willo Flood.
Michael Higdon takes a shot. Radoslaw Cierzniak makes a comfortable save.
Stevie Hammell takes the free kick.
Booking The referee books John Rankin for unsporting behaviour.
Jamie Murphy fouled by John Rankin, the ref awards a free kick.
Corner taken right-footed by Willo Flood, comfortable save by Darren Randolph.
Free kick taken by Willo Flood.
Substitution Gary Mackay-Steven replaces Richie Ryan.
Johnny Russell fouled by Nicky Law, the ref awards a free kick.
Inswinging corner taken from the right by-line by Stevie Hammell.
Johnny Russell has a curled shot. Save by Darren Randolph.
Shot by Richie Ryan. Clearance made by Stevie Hammell. Corner taken right-footed by Willo Flood from the left by-line, Darren Randolph makes a brilliant save. Willo Flood takes the outswinging corner, clearance by Stevie Hammell.
Stuart Armstrong takes a shot. Clearance by Tom Hateley. Willo Flood takes a outswinging corner from the right by-line to the near post, clearance by Tom Hateley.
Stuart Armstrong produces a right-footed shot from the edge of the box and misses to the right of the goal.
Tom Hateley produces a shot on goal direct from the free kick.
Booking Gavin Gunning is cautioned by the ref for unsporting behaviour.
Free kick awarded for an unfair challenge on Jamie Murphy by Gavin Gunning.
Effort from inside the box by Henrik Ojamaa bounces off the post.
Foul by Tom Hateley on Stuart Armstrong, free kick awarded. Direct strike on goal from the free kick comes in from Willo Flood, save made by Darren Randolph. Jon Daly concedes a free kick for a foul on Darren Randolph. Free kick taken by Darren Randolph.
The assistant referee flags for offside against Henrik Ojamaa. Free kick taken by Radoslaw Cierzniak.
Inswinging corner taken from the left by-line by Willo Flood, save by Darren Randolph.
John Rankin fouled by Nicky Law, the ref awards a free kick. Free kick taken by Keith Watson.
The official flags Michael Higdon offside. Free kick taken by Radoslaw Cierzniak.
The match restarts for the second half.
45:00 +0:03 Half time
Half Time The referee calls an end to the first half.
Shot from just outside the box by Henrik Ojamaa goes over the bar.
Corner taken by Stevie Hammell from the right by-line played to the near post, clearance by Brian McLean.
Gavin Gunning is adjudged to have handled the ball. Nicky Law takes the direct free kick.
Shot from just outside the area by Richie Ryan misses to the left of the target.
Henrik Ojamaa takes a shot. Corner taken by Stevie Hammell, clearance by Gavin Gunning.
Jon Daly challenges Simon Ramsden unfairly and gives away a free kick. Darren Randolph takes the direct free kick.
Keith Lasley has an effort at goal from outside the penalty area missing to the wide left of the goal.
Free kick awarded for an unfair challenge on Keith Watson by Henrik Ojamaa. Radoslaw Cierzniak takes the direct free kick.
Brian McLean challenges Chris Humphrey unfairly and gives away a free kick. Direct free kick taken by Tom Hateley.
Shot by Jamie Murphy from 18 yards. Keith Watson gets a block in.
Chris Humphrey has an effort at goal from just inside the box that misses to the right of the target.
Willo Flood takes a shot from 20 yards. Save made by Darren Randolph.
Unfair challenge on Keith Watson by Nicky Law results in a free kick. Gavin Gunning shoots direct from the free kick, save by Radoslaw Cierzniak. Stuart Armstrong takes a shot. Blocked by Darren Randolph. Willo Flood takes a inswinging corner to the near post.
Corner taken by Tom Hateley from the left by-line to the near post, clearance by Brian McLean. Short corner worked by Tom Hateley. Free kick awarded for an unfair challenge on Johnny Russell by Chris Humphrey. Direct free kick taken by Brian McLean.
Free kick awarded for a foul by Richie Ryan on Michael Higdon. Free kick taken by Michael Higdon.
Jamie Murphy has a drilled shot. Radoslaw Cierzniak makes a fantastic save. Short corner taken by Tom Hateley from the left by-line.
Henrik Ojamaa is caught offside. Radoslaw Cierzniak takes the free kick.
Cross/shot by Sean Dillon.
Free kick awarded for a foul by Keith Lasley on Johnny Russell. Free kick taken by Keith Watson.
Henrik Ojamaa produces a drilled right-footed shot from deep inside the penalty box which goes wide of the left-hand upright.
Stuart Armstrong produces a left-footed shot from just outside the penalty area that goes harmlessly over the target.
Inswinging corner taken left-footed by Stevie Hammell played to the near post, Jon Daly makes a clearance.
Jamie Murphy takes a shot. Save made by Radoslaw Cierzniak.
Johnny Russell takes the chance to get an effort at goal. Darren Randolph makes a save.
Jamie Murphy takes the chance to get an effort at goal. Radoslaw Cierzniak makes a save.
The ref blows the whistle to begin the match.
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