A Dane Murray own goal, Alexandros Kyziridis' stunning strike and Lawrence Shankland's penalty ensured the Scottish champions lost back-to-back league games for the first time in nearly two years.
Rangers are even further adrift as Hearts moved 16 points clear of the Ibrox side, who host Kilmarnock later on Sunday.
Not since Alex Ferguson led Aberdeen to the title in 1985 have Celtic or Rangers failed to win the Scottish top flight.
Hearts have been transformed since a minority investment in the club by Brighton owner Tony Bloom in June.
The expertise of Bloom's Jamestown Analytics firm has already reaped reward as summer signings Claudio Braga and Kyziridis again shone.
Hearts' title hopes have also been aided by a miserable time for both Glasgow giants.
Celtic's disastrous summer transfer window that has caused fan fury over a lack of investment is now being further exposed by an injury crisis.
Alistair Johnston, Cameron Carter-Vickers and Kelechi Iheanacho will all be sidelined for months after suffering serious injuries in Thursday's 2-1 Europa League win over Sturm Graz.
Carter-Vickers' replacement Murray suffered a torrid afternoon at Tynecastle.
The young centre-back sliced a Shankland cross horribly into his own goal to put Hearts in front on eight minutes.
Celtic responded immediately as Kieran Tierney teed up Callum McGregor to level.
Only a stunning save from Alexander Schwolow prevented Benjamin Nygren from giving the visitors a half-time lead.
But Celtic faded badly in the second period after their midweek European exertions as Hearts filled the home crowd with belief that the Old Firm stranglehold can be broken.
Kyziridis arrowed in a fine strike from outside the box seven minutes into the second half for his fifth goal since a move from Slovakian side Zemplin Michalovce.
Braga then tempted Murray into a naive challenge to give away a penalty, which Shankland confidently dispatched beyond Kasper Schmeichel.
Bloom, who was in attendance in Edinburgh, was then serenaded with chants of his name by the adoring Hearts faithful.
Only a fine Schmeichel save to deny Eduardo Ageu kept the score from becoming embarrassing for Celtic.
The Hoops have amassed 13 titles in the last 14 years during a miserable era for Rangers since their demotion to the fourth tier of Scottish football after going bust in 2012.
Now they finally face a new challenge as Hearts look to shake up Scottish football's stale duopoly.