Following up from last Wednesdayâ€™s 3-0 Scottish Cup win, the Steelmen managed to edged ahead of the Terrors despite having just three shots on goal to the visitorâ€™s nine.
Stuart McCallâ€™s men took the lead against the run of play in the 26th minute when Jamie Murphy pounced on a defensive error, advanced toward the byline and tried his luck from a tight angle which proved successful for his 11th of the season.
Dundee were searching for their seventh-straight league win and were making all the running but it was the home side who went two ahead just before half-time. Chris Humphrey ran at the United defence after taking possession about 40 yards out and then un leashing a shot which deflected off Sean Dillon and spun over United keeper Dusan Pernis to make it 2-0.
Peter Houstonâ€™s charges hit back with just over ten minutes remaining when Johnny Russell scored with a glancing header from a Paul Dixon corner and they then almost equalised in injury time but for â€˜Well gloveman Darren Randolphâ€™s top-shelf save from a David Goodwillie effort.