The Scottish champions took a surprise lead in the first half, with Javier Mascherano heading past his own goalkeeper after a superb delivery from Charlie Mulgrew wide on the right.
The hosts levelled the scores shortly before the break, though, when after an intricate move involving Xavi and Lionel Messi, Andres Iniesta stabbed the ball into the bottom right-hand corner.
And, with the game nearing its conclusion, Jordi Alba was on hand to break Celtic hearts by prodding home at the far post after beating his man for pace on the outside and latching onto an Adriano ball in the box.
Barcelona coach Tito Vilanova rang the changes for the game, bringing in young centre-back Marc Bartra for the suspended Sergio Busquets, while David Villa, Cesc Fabregas, Martin Montoya and Cristian Tello dropped out of the starting eleven to be replaced by Xavi, Adriano, Pedro and Alexis Sanchez.
Celtic manager Neil Lennon made four changes for the game, with Mikael Lustig, Emilio Izaguirre, Scott Brown and Georgios Samaras coming into the side for Adam Matthews, Tony Watt, Lassad Nouioui and Beram Kayal.
The hosts should have taken the lead as early as the second minute when a cute pass in behind the back four from Messi saw Sanchez miss a one-on-one chance, dinking his effort just past the left-hand post.
It was the unfancied visitors who took a shock lead in the 17th minute, though, when Mulgrew's viciously whipped free-kick from the right wing left Mascherano red-faced as he nodded into his own net under pressure from Samaras.
After finding themselves frustrated for the majority of the half, struggling to break down a stubborn Celtic defence, Barcelona drew level right on the stroke of half-time through Iniesta, who latched onto a magnificent through ball from Xavi to poke the ball past the onrushing Forster.
With Barcelona pushing for the lead, it took a world-class save from Forster to deny Messi who looked odds on to tap home from an offside position just six yards from goal after some good work by both Sanchez and Pedro.
Moments later, another high-quality save kept out a Messi header from point-blank range after a delicately clipped ball over the top from Xavi.
With the clock ticking down and Efe Ambrose and Kelvin Wilson excellent at the heart of the back four, Celtic got a deserved stroke of luck as Villa struck the post with an angled drive from within the box.
But the Bhoys' resolve was broken in the 93rd minute when Adriano's cross allowed Alba to steal in ahead of his marker and poke home.