Marius Niculae netted twice to break his Premier League duck as Inverness made it three wins in a row.
Niculae celebrates his first goal for Inverness
The Romanian international dinked a cool lob over keeper Yves Makalambay at the tail end of the first half.
Hibs rallied briefly in the second half and Clayton Donaldson was unlucky when his shot hit the crossbar and appeared to cross the goal-line.
But Inverness wrapped up the points when Niculae finished at the second attempt after some poor defending.
The victory was reward for a well-organised display, with midfielders John Rankin and Ian Black very impressive.
Hibs, who have been wretched in recent weeks after such a bright start to the season, have yet to score on any of their visits to the Caledonian Stadium
An untidy opening saw both sides struggle to build any momentum as passes went astray and players consistently lost their footing on the greasy surface.
Patrick Noubissie was making his Hibs debut and added some steel to the midfield, while playmaker Guillaume Beuzelin was left on the bench.
The game burst into life on 25 minutes when Hibs striker Steven Fletcher spun away from his marker on the edge of the penalty area but sprawling goalkeeper Michael Fraser managed to push the resulting shot away.
The home side responded with a lightening counter-attack and Rankin's long-range lob was brilliantly tipped away by the towering Makalambay.
Inverness looked marginally more menacing as a poor first half wore on and they were rewarded with a goal three minutes before the interval.
Rankin released Niculae with a neat flick and the Romanian striker calmly lifted the ball over the advancing Makalambay for his first league goal.
Hibs were struggling to break down the home side and introduced Beuzelin and Alan O'Brien early in the second half.
A Rankin screamer from distance fizzed over the crossbar before a flurry of activity in the Inverness penalty box.
Fraser saved a low shot from Fletcher and again used his legs to keep out Brian Kerr's side-foot volley.
Donaldson then burst through and, despite having his jersey pulled by Phil McGuire, managed to get a shot away, which came back off the underside of the crossbar and bounced out after crossing the goal-line.
The visitors were furious that referee Kenny Clark didn't award a goal and chose to do nothing about the infringement by the defender.
Black then saw a powerful shot whistle narrowly wide as Inverness sprung another good counter-attack.
Niculae grabbed his second goal on 78 minutes when Hibs fell apart at the back.
Graham Bayne flicked on a throw-in and the striker's first shot looked to be going wide before defender Darren McCormack slashed a wide clearance straight back to him and the forward slammed the ball back into the net.
The Romanian was denied a hat-trick in the final minutes when his 25-yard strike missed the target by inches.
Inverness CT: Fraser, Proctor, McGuire, Munro, Hastings, Cowie, Duncan (Wilson 85), Black, Rankin, McBain (Bayne 72), Niculae. Subs Not Used: Malkowski, McCaffrey, McAllister, Kerr, Vigurs.
Goals: Niculae 42, 78.
Hibernian: Ma-Kalambay, McCann, Hogg, Noubissie (Antoine-Curier 80), Murphy, Morais (Beuzelin 57), Kerr, McCormack, Stevenson (O'Brien 57), Donaldson, Fletcher. Subs Not Used: McNeil, Gathuessi, Joneleit, Zemmama.
Ref: K Clark