Needing a win to usurp the Jambos at the top of the table, Celtic came from behind to deny Hearts a first title in 66 years.
The Jambos were within minutes of ending the stranglehold on the Scottish game exerted by Rangers and Celtic, which now extends to 41 years.
Derek McInnes’ men took the lead when Lawrence Shankland headed home a corner in the 43rd minute.
Celtic rallied to level before the break courtesy of an Arne Engels penalty in stoppage time.
Hearts resisted during an incredibly tense second half until three minutes from time, when Daizen Maeda bundled in.
The goal was initially ruled offside but a VAR review reversed that call.
Callum Osmand was then able to walk the ball in to the net with the final kick of the game after Hearts goalkeeper Alexander Schwolow came forward in the hunt for an equaliser.
Celtic fans spilled onto the pitch in celebration, but it was devastation for Hearts, who have once again fallen at the final hurdle.
A 2-0 defeat on the final day to Kilmarnock in 1965 saw them lose the league on goal average.
And 21 years later they were seven minutes away before Albert Kidd struck twice for Dundee and allowed Celtic to snatch the title on goal difference.
Face-off
Not since Rangers got the better of Aberdeen 35 years ago had the top two faced off for the title on the final day of a Scottish season.
Hearts boss McInnes said he expected “bedlam” with the visiting support less than 1,000 of the 60,000-capacity crowd at Celtic Park.
But the visitors dampened the atmosphere as McInnes’ gameplan worked a treat early on.
With so much on the line, the first half was frenetic and short on quality but Hearts took a crucial lead.
Celtic goalkeeper Viljami Sinisalo got caught under Stephen Kingsley’s corner and Shankland headed in at the far post.
The days before the match had been dominated by the fallout from a controversial late penalty that handed Celtic victory at Motherwell on Wednesday to keep Martin O’Neill’s men in the race.
McInnes branded that decision “disgusting”, but there were few protests when Hearts conceded a penalty in first-half stoppage time.
Kieran Tierney’s cross hit Alexandros Kyziridis’ outstretched hand just inside the area.
Arne Engels’ spot-kick squeezed under Schmolow to give Celtic hope.
The introduction of Kelechi Iheanacho finally gave Celtic some cutting edge as they hemmed Hearts in.
Iheanacho struck the base of the post and Schwolow tipped over Benjamin Nygren’s drive as the pressure built.
The dam finally burst when Maeda turned in Osmand’s cross only for the flag to briefly halt Celtic celebrations.
VAR again came to the Hoops’ aid.
Osmand then rubbed salt in the wounds for McInnes’ men by bursting clear from inside his own half to roll into an unguarded net.
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