Danny Johnson struck on his Dundee debut to send the Dark Blues into the Betfred Cup last 16 and dump Inverness out.
The former Motherwell striker grabbed the only goal of the Group D decider at Dens Park on 33 minutes.
After a cute reverse from Shaun Byrne, the 26-year-old fired a low shot underneath Caley keeper Mark Ridgers, who perhaps should have done better.
Championship rivals ICT end the group in second spot but that was not enough for them to earn a place in the knockout stages, with East Fife grabbing the final best-placed runners-up spot.
Dundee will face Aberdeen at Dens Park in the last 16 but now prepare for their league opener at Dunfermline on Friday night.