Goals in either half from Victor Wanyama and teenager Tony Watt, making his debut in the competition, secured a victory that even their staunchest of fans were not predicting against the Catalan giants.
The rain in Glasgow fell mainly on the men from Spain as 60,000 Celtic fans deliriously celebrated a result which caps this week's 125th anniversary of the club's founding.
Among the crowd were singer Rod Stewart, seen in tears at one point, and former Celtic manager Gordon Strachan, now linked to the Scottish manager's post.
The Parkhead men had to withstand the usual pressure from a Barcelona side, regarded by many as the best club team in the world, orchestrated by Messi, Xavi, Iniesta and their millionaire team-mates.
But a combination of stalwart defending, the woodwork, and good saves by Fraser Forster kept Barcelona at bay until the final minute of normal time, when Messi snatched a goal.
It was Barcelona's first defeat in a group stage game in three years.
Jubilant Celtic manager Neil Lennon managed the victory without three of his stars: captain Scott Brown, highly rated striker Gary Hooper, and full-back Emilio Izaguirre.
Lennon later described the result as "one of the proudest of his career" and paid tribute to the "monumental" efforts of his players.
He said: "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 Hoops fans will surely fancy their side's chances of reaching the knockout stages of the competition but Lennon remained cautious.
The former Celtic skipper said: "We have a chance, that's all it has given us. 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."