Jason Cummings netted for the 17th time this season and Farid El Alagui added a late second to keep Hibs at the front of the play-off queue in the second-tier.
After a frantic start to the match, Hibernian created the first chance on 12 minutes when Cummings controlled a cross from Martin Boyle at the near post and laid a pass back to Fraser Fyvie to shoot just beyond the far upright from 20 yards.
Two minutes later, the visitors survived a bigger scare when Liam Fontaine rose to meet a corner and his header thumped the crossbar with the Hearts’ defence static.
Hibernian were dictating the tempo and Cummings tested Neil Alexander on 25 minutes when he skipped inside Hearts captain Danny Wilson and crashed a shot towards the far corner, but the ‘keeper got across to push the ball away.
The breakthrough came half-an-hour in when Hearts failed to clear a corner and Fyvie nodded the ball back into the penalty area where El Alagui flicked on to the unmarked Cummings to touch over the line from close range.
Hibs came close again six minutes before the break from yet another corner, as Scott Allan’s delivery came off the head of a Hearts defender and Fontaine smashed a volley against the bar with ‘keeper Alexander beaten.
Three minutes after the interval, Jamie Walker was tripped by Fyvie just outside the Hibernian penalty area and Alim Ozturk beat the defensive wall with the free-kick but was a couple of feet wide of the target as well.
Hibernian goalkeeper Mark Oxley was finally called into action on 54 minutes when he tipped Walker’s dipping drive from 20 yards over the bar.
But Hibs squandered a wonderful opportunity to double their lead on 66 minutes when, from yet another corner, Jordan Forster controlled the ball on his chest and lofted a pass into the six-yard box where El Alagui lost his marker but got no power on his shot which he directed straight at Alexander.
The pattern was familiar to countless Edinburgh derbies in recent years, where Hibernian’s profligacy has ended up costing them dearly and Hearts have rescued a result.
And Hearts almost levelled when Walker arrived at the back post and nodded the ball back towards the penalty spot where Genero Zeefuik’s shot was blocked by Forster before the Hibs defence eventually cleared the danger.
Oxley had to be alert a few minutes later when Osman Sow found a yard of space just inside the box and swept a low shot on the turn which the ‘keeper got down to parry at his post.
But Hibernian were rewarded for their dominance on this occasion when Dominique Malonga got in behind the Hearts defence and lofted a pass to El Alagui and he kept his composure to dink the ball past the advancing Alexander in the final minute of the match.