Liam Craig's penalty gave Terry Butcher victory in his first Edinburgh derby as Hibs manager and left Hearts 16 points adrift at the foot of the Premiership.
The decisive spot-kick came after Hearts had battled back from a goal down.
James Collins gave Hibs a deserved lead by swivelling to fire high past Jamie MacDonald.
David Smith's shot for Hearts was carried into the net by defender Ryan McGivern but Craig had the last word.
And the three points moved Hibernian into the top six as Butcher guided the team he took over in November to a third straight win.
Their start to the match had been determined and, at times, frantic. However, that mirrored their opening to October's League Cup defeat by Hearts - a cause for anxiety among the home fans and one of hope for the visitors.
And those contrasting emotions were exacerbated when the visitors carved out the first genuine chance.
Callum Paterson crossed for his namesake Tapping to turn goalwards, forcing keeper Ben Williams to scramble clear.
Hibs responded and Craig's free-kick into a crowded area was helped on to the crossbar by the head of Jordon Forster.
The execution of Jason Cummings' final shot was wildly off target after his promising run into the box but his next effort, a looping header, forced MacDonald to tip over.
Collins' opportunistic strike put Hibs ahead
Referee Bobby Madden was unmoved by penalty claims for handball against Brad McKay after the Hearts defender blocked Collins' shot at the start of the second half.
Scott Robertson stooped to head narrowly wide of the Hearts goal moments later but the unrelenting pressure would finally tell.
Paul Hanlon's presence at a Craig corner unnerved the visiting defence and Collins picked up the scraps to score on the turn.
Hearts knew their game plan had to change and McKay, who started in place of the unwell Danny Wilson, headed Kevin McHattie's corner just wide.
And Smith provided some attacking impetus after he came on for Tapping.
The substitute dribbled away from several challenges on a mazy run from the left and, after his initial shot was saved, the rebound effort was deflected over the line by the unsuspecting McGivern.
The pendulum swung back towards Hibs and Jordan McGhee unnecessarily stuck out a leg as Lewis Stevenson chased a pass that was trickling out and Madden pointed to the spot.
Craig was composed from 12 yards but Hibs' work was not quite done.
Williams saved well after McHattie fired in from the left and substitute Paul Heffernan and Collins passed up decent chances to add to the Hibernian advantage in stoppage time.
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