The Tynecastle defeat leaves last season's Scottish Cup winners stuck in 10th place, seven points from the upper half of the Clydesdale Bank Premier League.
Terry Butcher's team, however, were able to regain second spot in the standings as they recorded just their second win in eight games.
The home side were undone by a Gary Warren double which came either side of Billy McKay's 22nd strike of the season.
Yet Hearts had twice equalised through Jason Holt and a deflected Andy Webster strike - but both times handed the initiative back to their Highland visitors within minutes.
The final whistle brought another round of boos from the maroon contingent amongst the 11,325-strong Gorgie crowd just a week after their team was dumped by Kilmarnock.
Hearts were able to include Darren Barr in their line-up even though he had been carried off on a stretcher with a suspected concussion during their 3-0 defeat to the Rugby Park side seven days ago.
The former Falkirk player suffered a sickening collision with team-mate Danny Wilson but made a remarkable recovery to take his place against Butcher's men.
Jambos boss John McGlynn did, however, make two changes to his line-up following that Killie calamity, with Arvydas Novikovas and Kevin McHattie replacing Scott Robinson and Billy King.
Butcher also reacted to the 3-0 loss imposed on his side by Motherwell a week ago by bringing Daniel Devine back into his starting line-up at the expense of defender Josh Meekings.
Those in attendance did not have to wait long for the first flashpoint as Caley Thistle's Warren involved himself in a tussle with Hearts strike Michael Ngoo after just 22 seconds and promptly found himself flat on his back following a two-handed shove by the on-loan Liverpool youth.
A booking was Ngoo's punishment for what was in truth a major over-reaction to a physical challenge but it was the visiting defender who came up with a much more meaningful contribution 16 minutes in.
Jambos centre-back Webster was dragged out to the left and in uncomfortable territory, opted to clip the heels of Aaron Doran as the Inverness wide man pushed forward.
From the free-kick, the victim picked out Warren's march into the area and the Englishman headed past a stationary Hearts stopper Jamie MacDonald.
The goalkeeper was equally motionless as Caley midfielder Owain Tudur Jones smashed another set-piece through his defensive wall three minutes later. Fortune was on his side this time, though, as the ball flew wide of his right-hand post.
Hearts were intent on playing through loan front man Ngoo but little stuck for the England Under-20 cap in the opening half an hour.
By contrast, Andrew Shinnie was looking increasingly influential for the Highlanders.
He was unlucky that team-mate McKay set off a second too soon after slipping a perfectly-measured through ball beyond the home defence, which the Northern Irish striker tucked past MacDonald before being called back by an offside flag.
The home side had come close only once in the opening period with an early Webster volley flying a good 10 feet over the bar. It was therefore with a hint of frustration that Barr sent an aimless right-footed shot wide of target three minutes from the break as Inverness continued to prove themselves stubborn opponents.
His mood would have darkened further three minutes after the interval when he failed to read the flight of Fraser Mullen's free-kick to the back post just as it looked perfectly set for him to stab home the leveller. The booking he collected for rugby-tackling Shinnie soon after hardly helped.
Relief, though, did come for Barr and his fellow Jambos on 55 minutes.
Arvydas Novikovas and Barr exchanged passes before the later rolled the ball square for Holt on the edge of the box. After evading Warren's challenge with a shoulder feint, he sent a well-hit shot with his right foot soaring past Ryan Esson in the away goal.
Parity lasted just seven minutes though as Inverness struck for a second time.
David Raven launched a free-kick from halfway into the box which Tudur Jones met with a firm header to pick out McKay lurking at the back post. The striker still had to beat Callum Tapping to the ball but found the required yard to nod home.
The hosts, though, responded again - but their second equaliser came with a heavy slice of luck.
First they won a disputed corner which Warren insisted should have been an Inverness goal-kick. It looked as though the visitors would escape unscathed though when Ngoo met the set-piece with a tremendous header only to see Nick Ross clear from underneath his own bar.
Hearts, however, remained alert and worked the ball back to Webster on the edge of the box and he volleyed past Esson but only after the ball took a huge change of course as it deflected off Devine.
Holt came close to another for the Edinburgh outfit as he hit an ambitious volley just over the top of Esson's frame but it was Caley who would strike for the third time.
Having failed to learn from their first-half lesson, Hearts let Warren run free again and he was full-blooded with his header past MacDonald from Graeme Shinnie's in-swinging corner to edge Inverness above Motherwell and into second place by a point.
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