The sell-out crowd witnessed a game with plenty of hard work, fouls and competitivenes, while there was a lack of quality at times.
Ian Harkes came up with the defining moment, turning on the edge of the box to fire past Adam Legzdins. There were some big performances for the Tangeroines, especially in defence and midfielder Jeando Fuchs.
It is the latest big win for Thomas Courts this season after victories over double winners St Johnstone and Scottish champions Rangers.
How did the United players rate out of ten?
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
1. Benjamin Siegrist - 7
Returned to the starting XI was a calm presence in goal, with good handling. Made a decent save from Griffiths early in the match. Photo: Ross Parker - SNS Group
2. Kerr Smith - 6
Tricky afternoon for the 16-year-old defender, who was clearly targeted by Dundee as an area of exploitation. Largely stood firm, but appeared to be injured early in the second half and was replaced after a yellow card. Photo: Alan Harvey - SNS Group
3. Ryan Edwards - 8
Threw himself in front of a Byrne effort to stop it going in and cleared Marshall's shot off the line in stoppage time. Very impressive performance. Photo: Paul Devlin - SNS Group
4. Charlie Mulgrew - 8
Huge late tackle on Sheridan denied Dundee a late equaliser. Very few errors in defence and also came close with long-range free-kick. Photo: Mark Scates - SNS Group