Neil Lennon's side enjoyed a fabulous win in what will go down as one of the biggest upsets ever in the competition against Tito Vilanova's out-of-sorts outfit
The hosts took a shock lead in the first half through a Victor Wanyama header after a beautifully curled in Charlie Mulgrew corner, getting the better of left back Jordi Alba in the air to nod home.
Despite its pressure throughout, it was Celtic that grabbed that crucial second goal late in the second half with forward Tony Watt latching on to the long ball, outpacing Javier Mascherano before coolly slotting home into the far corner.
Barcelona managed to grab a late goal back through Lionel Messi after Fraser Forster turned away a Pedro strike from close range, before the Argentina international followed up to lash home.
Celtic manager Neil Lennon made four changes to the team that drew with Dundee United in the club's last outing, drafting in Efe Ambrose, Mikael Lustig, Miku and Georgios Samaras into the side for Emilio Izaguirre, Tony Watt, Thomas Rogne and Scott Brown. Striker Gary Hooper missed out altogether after failing to recover from a hamstring injury.
Barcelona boss Tito Vilanova also made four changes to the side that beat Celta Vigo over the weekend, with Daniel Alves, Marc Bartra, Alex Song and Alexis Sanchez coming into the side for Adriano, Sergio Busquets, Cesc Fabregas and David Villa.
In a cagey opening, the visitors struggled to create anything of note and Celtic took the lead in the 20th minute through a Wanyama header at the back post after an excellent in-swinging Mulgrew corner from the right, beating fullback Alba in the air.
This prompted a response from Barcelona and Messi struck the bar from just inside the area shortly afterwards after a period of sustained pressure in the final third, only to see it fly over the bar on its way, while Alexis struck the foot of the post with a header from an Alves cross 10 minutes before the break.
After halftime, though, the game began to open up more with Barcelona peppering the Celtic area with wave after wave of attack and Alexis brought a terrific save out of Fraser Forster low to his right on the hour mark.
The constant probing and movement of Barcelona saw the Spanish club carve open the defense in the 70th minute and Messi forced another fantastic stop out of Forster after latching on to Alba's cut-back down the left before hitting a sweet strike towards the bottom right corner only to see the goalkeeper claw it away.
With the visitors piling on the pressure, it was Celtic which struck next in the 83rd minute when a long punt down field by Forster was missed by Xavi and Watt was through in on goal past Mascherano before rifling his strike into the bottom left-hand corner to hand his side a two-goal lead.
Barcelona wasn't finished there, though, and grabbed a goal back in the 90th minute through Messi after Forster parried a Pedro shot inside the six-yard box following an intricate, flowing move, leaving the forward to smah home high into the goal.
Nevertheless, despite some nervy moments late on with Barcelona flooding forward, Celtic was able to clinch the historic win in front of its own fans in what will go down as the team's best European result since winning the European Cup final back in 1967 against Inter Milan.