The lively Billy McKay bagged a first-half brace for the unbeaten hosts, and then had a second-half penalty saved after bottom club Hearts had Jamie Hamill sent off.
The hosts were soon on the front foot and Richie Foran put their first chance wide of the target before McKay (10) made no mistake two minutes later.
The forward was picked out by a fine first-time cross from Aaron Doran and produced a controlled shot which Jamie MacDonald could only help into the roof of the net.
Hearts tried to respond but, after good work from Calum Paterson, Gary Walker shot just wide from a tricky angle.
But Inverness then doubled their lead with a breakaway goal, McKay (32) finding the target with a curling shot after being found at the back post by James Vincent, who had latched onto the loose ball when a Doran effort was deflected.
The score-line was a little harsh on the visitors and they almost got back into the game just before the interval when Graeme Shinnie lost possession on the edge of the area to Walker, who unleashed a shot which came back off the post.
Walker had another opportunity soon after the interval but shot well wide after storming through the middle.
Warren hits the crossbar
However, Hearts then had a lucky escape when Gary Warren's header from Doran's cross came back off the crossbar and Vincent then shot wide when McKay played the ball back into the danger area.
And McKay twice went close to completing his hat-trick soon afterwards, cleverly flicking a Nick Ross cross inches wide of the far post before testing MacDonald with a volley.
It was essentially one-way traffic by this point and MacDonald again did well to keep out a long-range Foran piledriver, before Doran shot just over from a narrow angle after chasing down a throw-in and then fired wide from the edge of the area.
McKay continued to squander chances, trying to go round MacDonald when through on goal but failing to make room for a shot.
And the inspired Hearts goalkeeper then dived to his right to keep out McKay's penalty 10 minutes from time after Hamill saw red for a deliberate handball.
The decision may have been harsh, Hamill punished for blocking McKay's effort after MacDonald had brilliantly foiled Foran.