The underdogs stunned the Catalan giants in the 21st minute when midfielder Victor Wanyama rose at the back post to bullet home a Charlie Mulgrew corner.
Celtic had to defend for most of the night as the visitors hit the woodwork twice and keeper Fraser Forster pulled off a couple of vital saves.
However, in the 83rd minute 18-year-old Tony Watt raced away to score the second, leaving Lionel Messi's late strike a consolation.
The Celtic manager could hardly suppress his joy afterwards, saying: "I think it was one of the greatest nights in the club's recent history.
"It was very poignant at our 125th anniversary, one to play Barcelona in such a prestigious game and two, to win the game under huge difficulties with the squad decimated by injuries and illness.
"The players are heroes, they are heroes to me, I can't speak highly enough of their performance tonight and they will go down in the history books of the club as the team who beat probably the best team in the world.
"Everyone goes on about tactics but football is about players and they have covered themselves in glory tonight."
Celtic, with seven points from four games, two less than leaders Barca, travel to Benfica before hosting Spartak Moscow in their final group fixture.
Benfica have four points following their home win over Spartak Moscow, who are bottom of the group with three points.
The Celtic fans will surely fancy their side's chances of reaching the knockout stages of the competition but Lennon remained cautious.
"We have a chance, that's all it has given us," he said. "A greater chance than maybe we expected before the game. But we still have two very tough games.
"The problem is the players and staff will have to deal with is that the expectation level will increase.
"There is still a lot of work to do but we have given ourselves a platform.
"But that's for the future, I want the players to enjoy the moment and take it all in."
Barca coach Tito Vilanova said: "First of all I would like to congratulate Celtic, the fans were amazing tonight.
"Before we played I knew they were good at set pieces and we didn't want to concede too many and we didn't give them too many chances.
"But I can't be satisfied because we want to win the game.
"It is a really difficult stadium but we were like the home team and we locked them in the box.
"But you are never happy when you don't win.
"If we had scored first it might have been a different game.
"But they scored first which allowed them to defend and their goalkeeper was brilliant tonight.
"It is not the first time we have lost a game like this and it won't be the last."
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