Russell sent a looping header into the far corner from Keith Watson's 84th-minute cross as Peter Houston's side moved level on points with Motherwell in seventh place following their fourth consecutive Clydesdale Bank Premier League match without defeat.
Motherwell striker Henrik Ojamaa had twice hit the frame of the goal as the hosts dominated the middle part of the contest, but United came into it in the final quarter and snatched victory in a game originally postponed because of a power cut.
The 3,941 fans who turned out again witnessed some decent attacking play from both teams but Ojamaa found luck against him as he continued to seek his first goal of the season.
Neither side looked content with a point and it was United who made the breakthrough.
Watson sent in a cross from just inside the Motherwell half over the head of Motherwell centre-back Adam Cummins and Russell looped a header from a tight angle over the head of Randolph and into the far corner.