Dundee manager Jim Duffy handed new signing Tom McManus a starting slot with top scorer Steve Lovelll missing through suspension.
The visitors started brightly, and only a last-gasp punch by Derek Soutar after five minutes directed Roy McBain's corner away from the goalmouth.
After 15 minutes Inverness's Craig Brewster shot wide of the target when in a good position before Graham Bayne was denied by Soutar from close range as the visitors looked to make their possession count.
Much against the run of play, Dundee took the lead after 28 minutes. It was a goal out of nothing as there looked little danger when Steven Robb collected the ball on the left, but the Dundee midfield ran past three defenders before poking the ball goalwards. Mark Brown should have done better than allow the ball to sneak under his body and into the back of the net.
Just before half-time Barry Wilson was unlucky not to get his name on the scoresheet for the visitors when firstly he headed agonisingly past the post before Soutar produced an excellent save to turn his deflected drive for a corner.
New Dundee signing McManus doubled Dundee's lead three minutes after the interval with a simple nod into the net from three yards after Brown could only parry Fabian Caballero's stinging 20-yard shot.
With 59 minutes gone Dundee put the game out of the visitors reach when John Sutton scored from the penalty spot after Stuart McCaffrey was penalised for hand ball inside the area.
The visitors had plenty more chances in the remainder of the game, but a combination of terrible finishing and great goal-keeping meant they were never going to claw back the three-goal deficitand. They did, however, have a last minute goal from Brewster to show for their efforts.