The Jambos began the day six points clear at the top of the table as they aim to break a 40-year stranglehold of Scottish football by Celtic and Rangers.
However, they suffered just a second defeat in 24 matches since the appointment of Derek McInnes as manager and a major investment by Brighton owner Tony Bloom transformed the club's fortunes.
Hearts never recovered from a nightmare start at Easter Road when Jamie McGrath steered home Nicky Cadden's cross.
Victory hauls Hibs back into the running for the European places as they close to within two points of third-placed Motherwell.
But inflicting a serious blow to their cross city rivals' title dream made the three points all the sweeter for David Gray's side.
Josh Campbell headed in a second just before half-time.
Kieron Bowie's strike three minutes into the second period then had some Hearts fans heading for the exit.
Yet, those that stayed nearly witnessed a memorable fightback.
Lawrence Shankland cut the arrears 15 minutes from time before Cammy Devlin set up a grandstand finish.
Hibs goalkeeper Raphael Sallinger needed to make impressive stops to deny Shankland and Beni Baningime as the home side clung on during six minutes of stoppage time.
The Old Firm duo can now close in on the leaders later on Saturday.
Celtic travel to bottom-of-the-table Livingston, while fourth plays third when Rangers host Motherwell.