Eoin Doyle's opener and a terrific strike from David Wotherspoon had given the home side a comfortable advantage. However, Conor Pepper pulled one back before Richie Foran grabbed a late equaliser.
Inverness remain without a league win this season, but they had cause to be happy with a point from contest that should have been over by half-time.
Hibernian's leading scorer, Leigh Griffiths, missed out with an ankle injury as manager Pat Fenlon opted for Ross Caldwell ahead of Shefki Kuqi in attack.
For Inverness, Owain Tudur Jones started his three-match suspension after being sent off in the 1-1 home draw against Aberdeen last Saturday. Pepper was his replacement.
Hibernian started the livelier with Josh Meekings fortunate to see a Wotherspoon shot shave the outside of the post after the defender inexplicably dummied the effort.
Wotherspoon's perfectly weighted through-ball then gave Doyle the chance to cross for Caldwell, who fired into the side-netting.
Inverness almost took the lead out of nothing when a sliding Aaron Doran shot forced a one-handed save from Ben Williams.
Straight from that passage of play Hibernian took the lead.
Paul Cairney's ball over the top utilised Doyle's pace as he outsprinted his marker and charged into the penalty area. The striker's initial shot was blocked by Ryan Esson but he was able to force the rebound over the line.
The architect of that goal was then unlucky not to get on the scoresheet, Cairney seeing his shot from 20 yards beat Esson but come crashing back off the goalkeeper's left-hand post.
Esson and Inverness' luck only lasted so long as Wotherspoon doubled the home side's advantage in spectacular style.
Allowed space 25 yards from goal, the Scotland under-21 international unleashed an unstoppable shot on the half-volley that found the top corner of the net.
After being denied once again by a low save from Williams, Inverness found a route back into the match after 38 minutes, albeit in controversial circumstances.
Alan Maybury hit the deck after being pressured by Pepper, but referee Euan Norris waved play on as the Inverness player raced through and drove his shot in off the far post.
Hibernian were clearly rattled by the incident and almost surrendered their lead a minute before half-time. Doran's clipped cross into the centre was powered goalward by Gary Warren, but the centre-back was denied by a strong one-handed stop from Williams.
Inverness pressed for a quick equaliser after the break but the first chance would fall to the hosts, with Caldwell sidefooting a volley high over the crossbar after being picked out by a Tim Clancy cross.
Hibernian should have wrapped up the points after 75 minutes.
Doyle's headed pass to McPake saw the defender chest and smash the ball on the turn inside the six-yard box. The Hibernian captain was denied by Esson throwing himself in front of the ball and diverting it for a corner.
The hosts had looked comfortable for most of the half, but saw all their hard work evaporate as one defensive lapse allowed Inverness to equalise.
Following a set-piece, Meekings collected the loose ball and took two defenders out of the game with a turn.
His shot was deflected into the path of Warren who, again, saw his effort superbly denied by Williams. However, in came Foran to smash the ball home off the underside of the crossbar.