Dundee did take the lead on 12 minutes when Ryan Sweeney got the fianal touch when the ball fell nicely after a corner from Grayson.
Inverness CT levelled a few minutes later with a finely taken goal but it looked bad from Dundee's point of view. Dundee kept up the pressure and had some chances but failed to take them.
Right on half time the visitors took the lead from the penalty spot after Sharp had fouled in the box.
The second half started well and within 11 minutes Dundee levelled when Joe Grayson touched the ball home after a good shot from McMullen. Midfielder Paul McGowan made all the difference after coming on for the second half, he replaced Ben Williamson.
Soon after Ashcroft was unlucky when his effort was cleared off the line. Mulligan and McMullan were denied by the ICT keeper who made good saves.
But the game was won by Inverness CT scored with six minutes to go after a slick move. Dundee's game was over when Ryan Sweeney was sent off after a silly foul earned a second yellow card.
Dundee: Sharp, French, Sweeney (c), Ashcroft, Marshall, Williamson (McGowan 55), McGhee, Grayson, McMullan, Mulligan (McGinn 69), Robinson (Rudden 69). Unused Subs: Legzdins (gk), Kerr, Sheridan, Anderson, Cameron, Strachan.
Att: 4,396
Referee: Peter Stuart
