Goals from Victor Wanyama and substitute Tony Watt earned Celtic a memorable win as they marked their 125th anniversary in style.
Lionel Messi pulled a goal back in stoppage time, but Celtic held on to take all three points and boost their chances of reaching the knockout stages.
Celtic, with seven points from four games, two less than leaders Barca, travel to Benfica before hosting Spartak Moscow in their final group fixture and will surely fancy their chances of reaching the knockout stages of the competition.
Regardless of the Scottish champions’ progress in Europe, the night will live long in the memory of the 60,000 who made their way to Celtic Park on a sodden night.
Barca were perhaps fortunate in the 18th minute when midfielder Alex Song, earlier booked for a challenge on Miku, fouled the same player and received no further punishment from referee Bjorn Kuipers.
However, the home fans were unconcerned about that when Wanyama gave them a sensational lead.