The twice European champions, who won their fifth straight match in the competition without conceding a goal, allowed Celtic plenty of possession but defended immaculately and looked dangerous every time they broke forward.
Despite resting several regulars, the Serie A leaders and champions completed the aggregate win with goals in each half from Alessandro Matri and Fabio Quagliarella, suggesting they are back as a force in European football after several years in the wilderness.
With Andrea Pirlo and Paul Pogba adding a touch of artistry in midfield and the compact, ultra-modern Juventus stadium providing an intimidating backdrop, they will be a team to avoid in the last eight.
"The difference is the quality in the final third of the field," conceded Celtic coach Neil Lennon. "We had good chances again tonight and we didn't take them.
"The difference was quality," he added. "Quality counts and that was what separated the two teams."
Juventus last reached the last 16 in the 2005/06 season, shortly before the Calciopoli match-fixing scandal blew up.
The club was stripped of their 2005 and 2006 Serie A titles, demoted to Serie B and spent the following few years rebuilding.
"We're all very happy to be back in the elite of European football," said Conte, who spent most of his playing career with the club. "We hope to continue in the right way."
SITTING BACK
Conte, who has been rotating his strikers all season, this time began with Matri and Quagliarella in attack while regulars Giorgio Chiellini, Stephan Lichtsteiner and Claudio Marchisio were all rested.
Celtic were far from outplayed in the first half, enjoying long periods of possession and giving Gianluigi Buffon several scares in the Juventus goal.
The hosts preferred to sit back and play on the counter, but looked like scoring every time they broke forward.
Their first goal came from one such move when Andrea Barzagli won the ball in midfield and released Quagliarella. Although his shot was saved by Fraser Forster, Matri was on hand to roll the ball into the net.
Arturo Vidal wasted two chances to increase Juve's lead before the break, sending an over-ambitious chip too high following a flowing move then shooting weakly at Forster after a run down the middle..
Celtic, who had threatened early with a rasping 30-metre drive from Joe Ledley could have equalised when Giorgos Samaras sent the ball flashing across the face of the goal, but nobody was on hand to turn it in.
Forster made a superb save to deny Matri at the start of the first half but was powerless in the 64th minute when Pirlo chipped the ball over the Celtic defence to Vidal, who rolled the ball for Quagliarella to score into an empty net.
