A second-half brace from Dennis Wyness was enough to see off a Hibs team that had a lot of the ball but couldn't find the final pass to unlock the Caley defence.
In an open but inspiration-lacking first half it was Caley Thistle that had the clearest chance but Zbigniew Malkowski did well to block Liam Fox's shot.
Although Hibs enjoyed the majority of possession they failed to test Mark Brown although he would have been relieved to see Garry O'Connor's lob land on the roof of the net after 15 minutes.
The second half started with a bang as both managers made it clear that a more direct approach was needed. Ivan Sproule was the first to respond and after breaking away from a Caley corner he beat his defender but his acute shot was saved by the legs of Brown.
Inverness didn't waste any time in replying. Barry Wilson angled in a shot that Malkowski couldn't hold only for Wyness to knock in the rebound.
The visitors continued to soak up the pressure and a second goal came via a long ball that Chris Hogg would probably like to forget.
With the ball bouncing high over the defender's head, Wyness nipped in and lobbed the stranded Malkowski.
Craig Brewster then saw red for two bookings before even more Hibs pressure finally brought a goal, Steven Fletcher nodding in from a corner but it would prove to be too little too late.