Garry O'Connor gave Hibs an unlikely Edinburgh derby win in a controversial encounter which yielded seven yellow cards and one red.
O'Connor struck deep into injury-time when he took a pass from fellow substitute Stephen Dobbie to score with a low right-foot shot.
But the Easter Road side face an SFA inquiry after a supporter raced on to the pitch as the teams went off at half-time and made for referee Stuart Dougal. There was also a pitch invasion at the end from fans jubilant at the late goal.
Dougal sent off Grant Brebner nine minutes before the break and it looked a harsh decision and the official left the field at the break to loud boos from the Hibs crowd.
Hearts' striker Mark De Vries shrugged off a thigh injury to take his place in the starting line-up to give Craig Levein a boost before kick-off.
Hearts dominated the early stages but failed to put Daniel Andersson under any serious pressure. Indeed, it was Hibs who had the first opening after 16 minutes when Tom McManus found Ian Murray in the area, but the midfielder sliced his shot wide.
Derek Riordan then had a shot from 25 yards but it was directly at Tepi Moilanen and the goalkeeper was untroubled.
Jarkko Wiss came closer midway through the first half when he pounced on a knock-down from Scott Brown to power in a shot which clipped the outside of the post.
Riordan then forced a good save from Moilanen with a low left-foot shot as Hibs took control. Murray tried to guide a 20-yard shot into the corner of the net from the resultant corner but Moilanen read the situation well and gathered the ball at his right-hand post.
Hearts' first attempt on target did not come until ten minutes from half-time and De Vries should have done better but his 15-yard shot was clutched by Andersson.
Then came Brebner's sending-off for a challenge on Robert Sloan which looked at worst a yellow card and even the Hearts players seemed stunned by the decision.
Phil Stamp came close early in the second half for Hearts with an ambitious 30-yard shot which flew past Andersson's left-hand post.
Andersson produced a one-handed save in the 62nd minute to keep out a half-volley from Scott Severin, before Dennis Wyness sent a far-post header over with the goal at his mercy.
Hibs snatched the points right at the death when O'Connor struck with a shot which beat Moilanen at his near post.