Celtic had erased an eight-point deficit to the Jambos during Martin O'Neil's interim spell in charge to start the day level on points and with a game in hand over Hearts.
Derek McInnes' men had failed to win their four previous games but spoiled Nancy's welcome to reignite their hopes of becoming the first side outside Celtic and Rangers to win the Scottish title in 40 years.
Celtic were left to rue not making more of a bright start as Daizen Maeda wasted two glorious chances to open the scoring.
The hosts struggled to cope with Nancy's change to his preferred 3-4-3 system and wilted after Hearts took the lead against the run of play just before half-time.
The Celtic defence appeared to stop, believing Claudio Braga was offside, before he fired beyond Kasper Schmeichel, and there was no flag to rescue Nancy’s men.
Oisin McEntee then powered home a second from a corner just after the hour mark.
The Scottish champions still had chances to salvage a point.
Arne Engels' header was brilliantly saved by Alexander Schwolow before Reo Hatate rattled the crossbar on the rebound.
Kieran Tierney did halve the deficit deep into stoppage time, but it was too little, too late as Celtic suffered just a second home league defeat in two years.
Hearts lead the league by three points with Rangers now only six points adrift of Celtic after they won 3-0 at Kilmarnock on Saturday.
Thousands of Celtic fans poured out of the stadium before full-time, with many questioning the timing of Nancy’s appointment on Wednesday, in the midst of a crucial run of fixtures.
After a Europa League visit from Roma on Thursday, the Hoops face St. Mirren in the League Cup final next weekend.