They were almost behind after three minutes when Ross Tokely's header thrust goalkeeper Andrew McNeil into early action, turning the effort over the bar.
It took the visitors 15 minutes to threaten, Steven Fletcher playing in John Rankin, but the former Caley Thistle player dragged his shot a yard wide from 12 yards.
Inverness, however, were playing the better football and they took the lead on 21 minutes following a sweeping move that began deep in their own half.
Ian Black's vision sent Don Cowie scampering away down the right and he cut inside, before unleashing a shot that found the corner of the Hibs, albeit a deflection off the boot of Chris Hogg took the ball beyond McNeil's reach.
Colin Nish then spurned a wonderful opportunity to equalise after 28 minutes as he took advantage of a square-looking Caley Thistle defence to run through on goal, but he ballooned his volley over the bar with only Michael Fraser to beat.
Three minutes later, Fraser's services were called upon, although much of it was through his own making. Having fumbled an effort from 18 yards by Fletcher, he was then forced to make another block at the feet of Dean Shiels.
Manager Mixu Paatelainen would have been pleased by the response from his side before the interval and they could even had went in on level terms had Fletcher connected better with Alan O'Brien's cross.
Hibs, however, took only 30 seconds of the second half before deservedly getting themselves back on level terms and scoring their first goal at Inverness into the process, Nish making up for his earlier miss with a composed finish for his third goal of the season after O'Brien's shot had deflected into his path.
Nish then went close to scoring his second of the day after getting on the end of O'Brien's cross only to see his effort rebound to safety via the post.
Caley Thistle were no having to weather the storm, although they did go close themselves with Phil McGuire forcing McNeil into a good save from his close range header.
Hibs did have a chance to win the game late on when Nish set up the unmarked Dean Shiels, but he rather rushed his shot and skewed it well wide of the goal.