Trailing to a Lee Miller goal at half-time, they hit back with late strikes from Garry O'Connor and Dean Shiels to snatch an unlikely victory.
Both sides were looking to recover from Scottish Cup semi-final defeats at the weekend and Hearts were more prominent in a frantic first half.
Paul Hartley whipped in an early free-kick which was too close to Simon Brown and then Miller miscontrolled a through pass from Neil MacFarlane when Hibs were caught short at the back.
Hibs' only early efforts were wayward from O'Connor and Hearts always carried more goal threat.
A fine pass from Deividas Cesnauskis picked out Mark Burchill but he failed to control the ball and another chance was lost.
It took a timely goal-line clearance from Antonio Murray to prevent a Miller header going in at the far post from a Jamie McAllister corner, but the same combination was to be Hibs' undoing later in the half.
Shiels had a decent opportunity at the other end after a well-worked corner between Derek Riordan and Stephen Glass.
The midfielder lost his marker in the area, but curled his final shot well wide of target when he had time and space to do much better.
Shortly afterwards, Gary Caldwell was caught out and Hartley homed in on goal, but once again his shot was directed straight at Simon Brown.
Both Ian Murray and Riordan were booked in the first-half for late challenges and, just as it looked as if the first half would finish goalless, Hearts were gifted a goal after 39 minutes.
McAllister's free-kick was headed on by Miller and goalkeeper Simon Brown misjudged the ball as it dropped in at his far post.
It was a bad goal to lose at a bad time and it ensured that Hearts approached the second half confident they could go on and secure the victory.
Burchill tested the positioning of Simon Brown at the start of the second half with a shot from the edge of the area which the goalkeeper saved comfortably.
Moments later, it took a wonderful reaction save from Craig Gordon to keep Hearts in front.
Hearts failed to clear a Glass free-kick and when the ball broke to Ian Murray his 16-yard shot was anticipated by Gordon who managed to beat the ball away.
Riordan felt he had equalised after he filched the ball from Gordon but the referee ruled he had fouled the goalkeeper.
Simon Brown made a fine save to keep out a 20-yard effort from Hartley with the Hibs defence opening up invitingly.
Hibs were level in the 68th minute with another gift-wrapped goal. Amadou Konte's cross caused confusion between Gordon and Jason Thomson and the ball broke to O'Connor, who rolled the ball home.
Remarkably, Hibs were in front five minutes later when Konte headed a Steven Whittaker cross against the post and Shiels followed up to lash the ball high into the net.