A much-changed home side surged into a two-goal interval lead when the 16-year-old Harry Cochrane fired in his first goal for the Edinburgh club in the 26th minute before the former Rangers striker Kyle Lafferty added a second with a fine finish nine minutes later.
David Milinkovic took advantage of some awful Celtic defending to make it 3-0 early in the second half, before wrapping things up from the penalty spot.
Celtic appeared unsettled and were slapdash in possession under heavy pressure from Hearts' aggressive pressing.
The Tynecastle side hammered Celtic 4-0, inflicting their first defeat by a Scottish opponent since May 2016.
Celtic, who Rodgers led to the Scottish Premiership, Scottish Cup and Scottish League treble last season, remain top of the league table by two points, with a game in hand over second-placed Aberdeen.
At the other end, Griffiths slipped when set up by James Forrest inside the Jambos' penalty box, then fired a similar opportunity into the side-netting.More news: McGregor Reacts To Pacquaio Boxing Match Speculation
Shortly after, Hearts netted another beauty, as Lafferty lashed home a low, angled shot from all of 20 yards, thundering into the post and bouncing back in.
The former Liverpool boss told Sky Sports 2: "Credit to Hearts, they were the better team, they were physically better than us in the first half and thoroughly deserved it. Congratulations to them on their victory".
Milinkovic also scored Hearts fourth in the 76th minute via the penalty spot after Ross Callachan was brought down by Craig Gordon.More news: 1 killed as natural disaster of magnitude 6.5 strikes Indonesia; tsunami warning issued
The performance of 16-year-old Cochrane was particularly eye catching, with Celtic bereft of a player who was able to make such an impression on the game as the scorer of the opening goal.
However, it was all going wrong for Celtic.
Brendan Rodgers' men looked tired and jaded after a punishing season already on the home and Euro front - but Lustig's delighted they've got a game again so soon.More news: CDC allegedly banned from using "science-based" and other phrases
- Verdict Day: All eyes on Gujarat, Himachal Pradesh today
- Ryan Reynolds Trolls Disney With This Cheeky Deadpool Photo
- Omarosa Manigault Newman 'physically dragged' from White House, reports say
- NBC Reportedly Paid Off Producer Who Accused Chris Matthews of Sexual Harassment
- Five Observations From Ravens' Win Vs. Browns
- Parliament winter session: Centre targets 25 bills over 22 days
- Jeremy Lin congratulates 16-year-old viral Harvard passer
- Jason Priestley Says He Punched Harvey Weinstein In The Face In 1995
- Oil prices hold steady on competitive data, North Sea outage
- Geminid meteors shower the skies