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.