Jason Cummings and Farid El Alagui struck as Hibs clinched their first derby win of the season.
Cummings claimed his 17th goal of the season, the teenager scoring in the 29th minute of a first half which was totally dominated by the home side.
That goal looked like being enough but El Alagui was left with only Hearts goalkeeper Neil Alexander to beat as the game moved into added-on time to clinched a vital three points for Hibs in their bid to finish second in the Championship table.
As Hibs ran Hearts ragged, Jambos defender Callum Paterson saw a header strike his own bar before Cummings netted. Hibs went close again when Liam Fontaine’s volley crashed back off the bar with goalkeeper Alexander beaten.
Robbie Neilson’s side were disappointing throughout that first 45 minutes but rallied after the break.
The game was barely a minute old before Scott Allan and Adam Eckersley were exchanging pleasantries on the touchline, the pair going head-to-head with referee Kevin Clancy keeping a close eye on the incident but deciding he had no need to intervene.
Hearts may be champions but Hibs went into this match in more need of the points and Alan Stubbs’ players took a grip of proceedings from the off although it did take a timely challenge from Paul Hanlon on the edge of his own penalty area to halt Genero Zeefuik.
It was, though, a rare moment of concern for Hibs, Fraser Fyvie fizzing one over from Cummings’ layback before the home side went even closer, Scott Allan’s free-kick catching the head of Paterson, who could only look on in despair as the ball cleared his goalkeeper only to clip the top of the bar and go over.
From the resulting corner, Fontaine saw his close-range shot blocked by a combination of Eckersley and Alim Ozturk.
Alexander threw himself to his left to push away a Cummings shot but the teenager set the home fans alight when he broke the deadlock in the 29th minute. El Alagui got on the end of Fyvie’s ball into the box, knocking it down for Cummings to score right-footed from only four yards out.
And Hibs might have been two ahead nine minutes later when Fontaine met Allan’s corner on the volley, only to see his shot crash back off the bar with Alexander beaten.
A Dylan McGeouch foul on Jamie Walker 23 yards out gave Ozturk a rare sight of the Hibs goal four minutes after the restart, but the defender, who had scored that memorable, last-gasp equaliser on his last visit to Easter Road, drilled his shot well wide of target.
Hibs fans were left raging when ref Clancy waved away claims for a penalty after Ozturk appeared to wrap his arm around the neck of Cummings as they chased down a long ball as Hearts, having failed to turn up in that first half, set about trying to get themselves back on level terms.
Mark Oxley was called on for his first serious bit of action, tipping over a powerful shot from Jamie Walker which was threatening to creep in under his bar.
Hibs’ passing certainly wasn’t as crisp and accurate as it had been in those opening 45 minutes and it took a neat piece of covering from Fyvie to halt Osman Sow as he burrowed into the home side’s penalty area in search of that equaliser.
El Alagui, however, passed up a glorious opportunity to score a second for Hibs, the striker unable to get enough on his shot when Jordon Forster’s ball left him with only Alexander to beat.
Stubbs, though, would have been becoming concerned at the number of free-kicks his side were giving away around their penalty area and it took a fantastic block by Forster to keep out Zeefuik’s shot which appeared destined for the back of the net.
Substitute Dominique Malonga wasted a promising opportunity for Hibs, electing to go it alone when he had team-mate Martin Boyle free in acres of space before Sow tested Oxley with a low shot which the keeper parried.
But El Alagui was to have the last word, scoring his first goal since returning from six months out with a ruptured achilles tendon to send the home fans wild.
Hibs: Oxley, Forster, Hanlon, Fontaine, Boyle, S Allan, Fyvie, McGeouch, Stevenson, Cummings (Malonga 68) (Dja Djedje 87), El Alagui. Unused subs: Cerny, Craig, Stanton, Handling, Dunsmore.
Hearts: Alexander, Ozturk, Wilson, McHattie (Nicholson 37), Paterson, Pallardo, Gomis, Eckersley, Walker, Sow, Zeefuik (King 77). Unused subs: Gallacher, El Hassnaoui, Keatings, Anderson, McKay.
Referee: Kevin Clancy.