The Italian champions, who again lead Serie A despite a recent wobble, were dominated by Celtic in the first half as the Scots besieged the Juve goal and harried every player as they were roared on by almost 60,000 passionate fans.
Juve took a third-minute lead through Alessandro Matri before weathering the storm to wrap up the win and their highly probable passage to the quarter-finals through Claudio Marchisio and Mirko Vucinic in the second half.
Conte, banned for 10 months in August for failing to report match-fixing at ex-club Siena before having his sanction slashed to four months in October, knows the second leg in Turin on March 6 should only be a formality but gave credit to Celtic.
"It has been a very important victory but also one where we suffered. Celtic are a great team when they play at home," Conte told Italy's Sky television.
"I didn't play in a hell like this many times," added the former Juve midfielder, who was in the team when they won their second European Cup in 1996.
"My lads have been superb, it was not easy to play in this atmosphere. We've managed a great result which proves this team has top technical and human values.
"Celtic are not, as a name, among the very best in Europe but it is not an accident that Barcelona lost here in Glasgow and that they eliminated Benfica (in the group stage) who are top of the Portuguese league."
The furious pace of the first half and a number of player spats added to the electric atmosphere but Celtic manager Neil Lennon felt his side could have had at least two penalties with Stephan Lichtsteiner grappling with Gary Hooper at corners.
"I'd like to ask the referee is the game different in Spain and Italy? Every time my player moved in the area it was a foul," he asked of Spanish referee Alberto Undiano Mallenco.