Coming into the game 22 points adrift of 11th-placed St Mirren in the Scottish Premiership with eight games remaining, Gary Locke's men knew defeat against their neighbours would see them consigned to the Championship.
However, goals from Dale Carrick and Billy King did enough to restore a measure of pride around Tynecastle against the 10 men of Hibs, who saw Alan Maybury sent off a minute from the end for a second bookable offence.
Hibs will feel aggrieved not to have earned a point, after Jordon Foster headed home with 10 minutes to go with the score still at 1-0, only for the referees' assistant to flag for offside when replays showed Foster to have been played on by a couple of yards.
Hibs pressed hard in the second half and ought to have been level when Foster's goal was wrongly ruled out.
