The visitors showed threat in the opening three minutes when Osman Sow cut in from the flank and attempted a through-ball for Danny Swanson, only to see his pass dealt with well by the Inverness defence.
Few chances followed, with Hearts defender Alim Ozturk failing to test Owain Fon Williams with a long-range shot over the bar from 35 yards, and Inverness midfielder Danny Williams allowing visiting keeper Neil Alexander to collect the ball with ease after a heavy touch in the box.
Caley Thistle's Greg Tansey then took aim from outside the Hearts box, but saw his low shot deflected once again into the arms of Alexander.
Hearts had similar luck, with Juwon Oshaniwa watching his shot smash into the side-netting with 10 minutes to go.
Williams had one final attempt for the home side before the half-time whistle, but his wide shot ensured that the game was goalless at the break.
Into the second half, and there was little wait for a goal as James Vincent put Inverness ahead from close range after four minutes.
Hearts winger Billy King looked to get his side back on equal terms 20 minutes later but watched his effort fly just over the bar, while midfielder Jamie Walker could only hit his shot wide of the post minutes later.
Both players had half-chances again shortly after, but Hearts were reduced to 10 men with three minutes to go as Oshaniwa was dismissed for violent conduct.
Inverness took full advantage of the situation, and secured the win with a second goal two minutes later as Miles Storey made it 2-0.
Hearts remain third in the Scottish Premiership, while Inverness move up to seventh.