Dundee made two changes to the team from Hamilton when Ben Williamson and Max Anderson came in for Joe Grayson and Josh Mulligan who were on the bench.
Dundee started well and had two efforts on goal from Zach Robinson and Ben Williamson's shot was deflected over the bar. But Dundee did take the lead on 10 minutes when from a corner was headed down by Lee Ashcroft and Max Anderson scored from six yards out.
A few minutes later and Robinson scored but the referee pulled it back for a foul. Cove came into the game and levelled when Megginson forced the ball home when the defence failed to clear the ball.
Both teams had chances up to half time but the best fell to Cove but their player put the ball well over the bar.
Second half and Rudden replaced Robinson who had been booked in the first half. Dundee had a early chance but Cove managed to clear, the game changed soon after when Scully scored with a volley from eight yards.
Four minutes and Scully all but sealed the point when he scored again. Dundee made changes to the team but failed to get back into the game, Cove looked like they could score more on the break.
A poor result for the dark blues and they must get points when they travel to Gayfield on Saturday.
Dundee: Legzdins, Kerr, French, Ashcroft, McGhee (c), Williamson (Marshall 87), McMullan, Anderson (Mulligan 58), McGowan (Sheridan 58), Cameron (McCowan 58), Robinson (Rudden at half time). Unused Subs: Sharp (gk), Byrne, Strachan, Grayson.
Att: 1,322
Referee: Nick Walsh
