Just as they had done in the Nou Camp two weeks ago Celtic took the lead against the run of play when Victor Wanyama headed them ahead in the 21st minute.
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.
Messi 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 counterpart Tito Vilanova praised Celtic in defeat.
"Congratulations to Celtic and their fans. The credit is theirs," Vilanova said.
"It was an amazing show. If we had scored first it would have been a more open match. We hit the post twice but their goalkeeper did very well."
Celtic, who gained revenge for their stoppage time 2-1 defeat in the Nou Camp, now sit second in Group G on seven points just two behind the Catalan giants and could qualify with a game to spare if they get a score draw or better against Benfica in two weeks time.
With several first team players already missing Celtic had been dealt another blow before kick-off when skipper Scott Brown was ruled out with a virus and Gary Hooper failed to recover from injury.
Barcelona had their own injury problems to deal with in defence but Gerard Pique found a place on the bench for the first time since September.
The Catalan giants had dominated possession at the Nou Camp and also did so in Glasgow - but to no avail.
After earning Celtic their first corner of the match Charlie Mulgrew fizzed his delivery to the back post where Wanyama rose above Marc Bartra to thump a header past Victor Valdes.
Following that it was all one-traffic towards the Celtic goal.
Messi came close to equalising when he collected a pass from Andres Iniesta in the box before cracking a half-volley off the bar.
Alexis then saw an angled header cannon off the base of the post in another let-off for Celtic.
The Hoops continued to frustrate Spain's league leaders after the break.
Forster again showed his worth when he got down smartly to stop a drilled strike from Alexis and then made a second save with his legs to deny the Chilean forward.
He produced more heroics in the 70th minute when he produced a superb one-handed save to stop Messi's strike from 10 yards.
Unbelievably, Celtic then increased their lead in the 83rd minute. Forster saved a Messi free-kick and his long kick out was then missed by Xavi to allow substitute Watt to get behind Javier Mascherano and drill a shot beyond Valdes.
Messi pulled one back in stoppage time after Forster had done well to keep out sub Cesc Fabregas' shot as the Argentine reacted quickest to lift the ball into the net from five yards.