Barcelona, who have made a record breaking start to their domestic campaign and hadn't previously lost in the group stages for over three years, dominated possession but lacked a cutting edge in front of goal with Lionel Messi hitting the crossbar and Alexis Sanchez heading against the post in the first half.
Fraser Forster produced heroics in the Celtic goal to deny Barcelona with the keeper superbly stopping further efforts from Alexis and Messi after the break. Celtic's chances were few and far between but they increased their lead in the 83rd minute when teenager Tony Watt, on as a substitute, scored a breakaway goal just 11 minutes into his Champions League debut.
On TargetMessi gave Barca hope in stoppage time when he pulled one back but the Hoops held on for a famous win the day after the club celebrated its 125th birthday to leave coach Neil Lennon a happy man. "It is one of the proudest nights of my career," the Celtic manager said. "It was just a monumental effort from all these players tonight.
"I wanted them to do themselves justice and they have even surpassed that. They have just beaten the best team in the world and, on the anniversary of the club, it is a very special occasion."
Barcelona coach Tito Vilanova praised Celtic in defeat. "Congratulations to Celtic and their fans. The credit is theirs," he said. "If we had scored first it would have been a more open match. We hit the post twice but their goalkeeper did very well."