After a goalless first half, Inverness drew first blood when Greg Tansey netted the Highlanders' first penalty of the season on the hour mark.
Paul Hanlon levelled with a close-range header four minutes later before Garry O'Connor put Hibernian in front in the 75th minute.
Jonny Hayes then equalised with a stunning cross-shot on 83 minutes before Leigh Griffiths bagged the winner for Hibs with a low angled effort from 12 yards with just five minutes to go.
Second-bottom Hibernian are now six points above bottom-placed Dunfermline and five behind Caley Thistle immediately above them.
The Edinburgh side netted all three of the chances they managed to create throughout the whole match to inflict an eighth home defeat of the campaign on their opponents.
O'Connor was among four changes to the Hibs line-up which lost 2-0 at home to Dundee United last weekend.
James McPake, Ivan Sproule and Richie Towell also came in, replacing Jorge Claros, Tom Soares, Roy O'Donovan and George Francombe.
Hayes and Kenny Gillet returned from hamstring problems for Caley Thistle and Josh Meekings was back from suspension following the midweek home loss to St Johnstone, with Thomas Piermayr, Owain Tudur Jones and Shane Sutherland the men replaced.
Inverness started brightly and Graeme Shinnie tested Hibs keeper Graham Stack with a low shot after connecting with a Hayes cross.
The Irish midfielder was next to warm the hands of Stack who palmed over his angled shot after a pinpoint crossfield pass from Greg Tansey.
Inverness keeper Jonny Tuffey was fortunate O'Connor failed to capitalise on his poor clearance following a questionable back pass from Richie Foran.
It was the only real chance of the half for the visitors who were lucky not to fall behind moments later.
Billy McKay might have broken the deadlock after 33 minutes when he latched onto a Hayes through-ball, but with only Stack to beat the Northern Irish attacker hit the post and the ball rebounded to safety.
Stack was alert to gather Foran's through-ball on the stroke of half time, as McKay ran through again.
Hibs might have tested keeper Tuffey just after the interval when Griffiths whipped a low ball across the face of goal but it was beyond the reach of O'Connor.
Tansey opened the scoring on the hour with Inverness's first penalty of the season.
The Englishman made no mistake after McKay was felled by Hanlon following a Tansey corner.
Moments later Gregory Tade could have doubled the lead but Stack saved well and the Frenchman's overhead kick from the rebound went just wide.
Ross Tokely's acrobatic effort from a Foran cross was went inches over and Inverness squandered chances to build on their advantage.
The missed opportunities proved costly when Hanlon made amends immediately for conceding the penalty by levelling in the 64th minute.
Griffiths' corner found the defender unmarked and his diving header inside the six-yard box gave Tuffey no chance.
Then O'Connor put the visitors in front with 15 minutes left.
Matt Doherty's powerful run down the right to the byline was followed by a cut back to the striker who side-footed the ball past Tuffey from eight yards.
It was O'Connor's 13th goal of the season, a tally including a winner when the sides last met in Inverness at end of July last year.
Hayes' cross-shot from 30 yards out looped over Stack to square things after 83 minutes, setting up a dramatic finish.
Celebrations from the home fans were short-lived, though, as Griffiths restored the visitors' lead two minutes later.
The 21-year-old was calm and collected as he cut inside the box and fired an angled shot low and beyond Tuffey to seal maximum points for the Hibees.