Goals from David Proctor and Richie Foran saw the Highlanders cut the gap to second-bottom Falkirk to a single point.
It was only the second home league win of the season for an Inverness side rejuvenated by Terry Butcher, who has not lost any of his first four games in charge.
Caley Thistle boss Terry Butcher was without suspended midfielders Ian Black and Russell Duncan, who were replaced by former Hibs man Brian Kerr and Roy McBain.
For the visitors, captain Rob Jones and Denes Rosa both started the game, Colin Nish - who was on Friday linked with a move to an unnamed Chinese club - was among the substitutes, while Ian Murray and Kevin McCann missed out.
The visitors set up in a 4-2-3-1 formation as they hunted their first ever win at the Caledonian Stadium.
After a couple of nervy moments at the back, Hibs launched an attack which saw Steven Fletcher tee up Jonatan Johansson for a header which flashed just wide.
At the other end, Foran fired a free-kick just past the right-hand post.
The home side's pressure paid off in the 14th minute when Proctor slammed home a low shot after creative work from Dougie Imrie and Eric Odhiambo.
It was just the start Inverness needed as they aimed to trim the four-point gap to second-bottom Falkirk.
Hibs pushed on though and after 21 minutes Johansson beat the offside trap but, with just Ryan Esson to beat, he slid a low shot wide from the edge of the box.
Derek Riordan switched from the left to the right flank and his teasing cross was plucked out of the air by Esson.
Hibs were probing their way into the game but could not find their way through, much to their frustration.
In the closing moments of the first half, Foran saw an effort dip over the bar as he connected with Ross Tokely's cross.
Referee Alan Muir was frustrating Butcher and the home fans as several harsh challenges went unpunished just before the break.
Joe Keenan came on at the start of the second half, replacing Ross Chisholm for the visitors.
It was turning into a midfield battle, with both goalkeepers largely spectators in this tussle.
French ace Lionel Djebi-Zadi tried to carve open a chance for Inverness, but his cross evaded all his team-mates in the box.
However, the Highlanders did get their second goal after 64 minutes when Foran pounced at close range after Imrie's drive was not properly cleared after Kerr's free-kick caused chaos.
Caley Thistle were surging on for a killer third goal, but Hibs keeper Gregorz Szamotulski came out to cut out a Tokely delivery.
With the clock running down, the hosts seemed the most likely to add to their tally as the visitors struggled to threaten.
In the final minute, substitute Adam Rooney closed in on goal, but the danger was cleared.