Mirko Vucinic came off the bench to save a point for Juve with an easy tap-in just after the hour after Victor Ibarbo had given the visitors a shock 12th-minute lead with a wonderful individual goal.
Antonio Conte's league leaders have 87 points with one game to go while Cagliari are 11th on 44 points.
Juve achieved their record tally of 91 points in the 2005/06 season. They won the league that year but were stripped of the title and relegated to Serie B following a match-fixing affair that ripped Italian football apart.
"I'm a bit annoyed we didn't win. With a bit more effort we could have written another important page in our history," said defender Giorgio Chiellini.
Ibarbo's goal was the highlight of an entertaining match, the Colombia striker weaving between Claudio Marchisio and a seemingly disinterested Andrea Barzagli before squeezing the ball under goalkeeper Marco Storari.
It gave the Sardinians a positive end to the week after club president Massimo Cellino was handed a four-month ban for his part in the Is Arenas controversy.
Juve had complete control of the match and carved out a series of half chances.
Sebastian Giovinco came closest to levelling just after the half-hour when his free-kick hit the underside of the bar before bouncing to Arturo Vidal who blazed the rebound over.
Juve finally grabbed a deserved equaliser when substitute Vucinic netted after Vidal's header was tipped straight to his feet by Cagliari keeper Michael Agazzi.
While Ivo Pulga's side, and in particular Ibarbo, always looked dangerous on the break it was Juve who set up the game's best opportunities.
"Winning is always hard," said Conte. "You have to always work hard and never be satisfied because the moment you think you can rest because you've won two titles in a row you get a full stomach [and it is all over]."
In the late game, an Alejandro Gomez goal was enough for Catania to beat relegated Pescara 1-0 and leapfrog Inter Milan into eighth place on 55 points.
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