Mistakes by Celtic defender Efe Ambrose on Tuesday led to goals by Alessandro Matri in the third minute and Mirko Vučinić in the 83rd. Claudio Marchisio had scored the second at the end of a flowing team move by the Italian champions and current Serie A leaders in the 77th.
The score line was harsh on Celtic, which dominated the first half and most of the second, only to lack a cutting edge to beat Juventus goalkeeper Gianluigi Buffon.
The second leg is in Turin on March 6, when Juventus will look to finish the Scottish champions off and maintain its unbeaten run in this season's competition.
Antonio Conte's side will know it rode its luck in Glasgow, though.
Celtic showed by beating Barcelona in the group stage that the team is a match for anyone at its intimidating Celtic Park home, and it posed Juventus all sorts of problems with its relentless work rate and high pressing game.
Even Italy midfielder Andrea Pirlo, usually so composed and elegant in centre midfield, was clearly ruffled at being hustled and harried but Celtic couldn't find the finish to go with its build-up play.
And the hosts conceded avoidable goals at either end of the match.
Ambrose after Afcon
Ambrose was at fault for both the goals – and Celtic manager Neil Lennon may be regretting playing the Nigeria centre back on the day he landed in Scotland after more than a month away with his country at the Africa Nations Cup. He played in the 1-0 victory over Burkino Faso in the final on Sunday.
For the opener, Ambrose misjudged a routine ball forward to leave Matri clean though on goal. The striker poked a finish through goalkeeper Fraser Forster's legs and the ball crossed the line by the time Kelvin Wilson slid in to clear away.
Marchisio slammed the loose ball into the net for good measure – with the assistant referee yet to signal – but Matri was given the goal.
Ambrose then pondered too long on the ball before being robbed by Marchisio and he fed Vučinić, who slipped a low finish into the net. Ambrose hung his head in despair.
Celtic's response to conceding early had been very impressive, peppering Buffon's goal with shots throughout the first half. Kris Commons had a handful of chances while Victor Wanyama headed over from a corner just before halftime, which Juve would have been relieved to reach without conceding.
The decibel levels remained high for the second half, as did Celtic's dominance – but still Buffon's goal wasn't breached.
Commons skied a shot over before Ambrose headed a golden chance straight at Buffon when completely unmarked eight yards out.
Marchisio punished Celtic for its profligacy by adding the second goal, running onto Matri's slick through-ball, cutting inside and firing in a shot that Forster couldn't keep out. – AP