Celtic's victory meant they leapfrogged the Jambos and finished top of the table on 82 points, two ahead of Hearts in second, securing a record 56th Scottish title.
Martin O'Neill's side scored two late goals to steal the win the Hoops needed to deny Derek McInnes' team a fairytale first title since 1960.
Hearts initially looked on course when Lawrence Shankland headed them in front two minutes before the break, but Celtic responded deep into first-half stoppage time as Arne Engels converted from the spot.
An increasingly tense second period seemed destined for a stalemate, a result that would have handed Hearts the title, but Daizen Maeda bundled the ball home with three minutes left. The goal was initially disallowed for offside before a VAR review overturned the decision.
As Hearts pushed desperately for an equaliser, goalkeeper Alexander Schwolow joined an attack late on. The gamble backfired when Callum Osmand was left with a simple finish into an unguarded net with virtually the last kick.
The final whistle sparked celebrations among Celtic supporters, many of whom spilled onto the pitch, while Hearts were left to absorb another agonising near-miss.
A 2-0 defeat to Kilmarnock on the final day of the 1965 season saw them lose the title on goal average.
And 21 years later, they were seven minutes from glory before Albert Kidd struck twice for Dundee, allowing Celtic to snatch the title on goal difference.
