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.
The Catalans had conceded from a set-piece in the Nou Camp and looked equally ropey when the Kenyan rose above Jordi Alba at the back post to bullet in Mulgrew's corner from the right.
Tito Vilanova's side went up a couple of gears and hemmed Celtic in at the edge of their own penalty area and in the 29th minute Iniesta set up Messi and his first-time strike clipped the bar on the way over.
Moments later, Alexis Sanchez glanced a header from a Dani Alves cross off the post and Celtic Park breathed again.
The second half began in similar style to the first with Barca taking control, switching from left to right and back again.
In the 56th minute Messi tried to beat Forster with a left-footed curler from 20 yards but the England squad member was equal to the task and soon made a good save from Sanchez's angled drive after Messi had split open the defence.
Despite all their possession, Barcelona looked vulnerable at the back and Mulgrew might have punished them in the 63rd minute when he had a sight of goal but Bartra managed to block. Song was allowed another foul on Miku to the anger of the Celtic fans, before he was replaced by Cesc Fabregas, with Pique on for Bartra and Watt on for Lustig.
Before the substitutions, Forster flew through the air to make a great save from Messi.
Beram Kayal replaced Samaras with 10 minutes remaining before Forster made yet another save from Messi, this time from a 25-yard free-kick.
But there was much more drama when Watt escaped the Barca defence and Xavi from Forster's long ball before driving a right-footed shot past Victor Valdes to double Celtic's lead.There was bedlam inside Parkhead which gave way to some nerves when Messi scored from close range in the 90th minute after Forster had parried a strike from Pedro, but it was to be the home side's night, and a famous night at that.
|1||1st Half Goals||0|
|3||Shots on Target||8|
|1||Shots off Target||10|
|13.4||1st Half Poss.||86.6|
|16.3||2nd Half Poss.||83.7|