A disciplined defensive performance from Celtic saw the club keep the Catalan giants largely at bay, but the team was denied a historic draw in stoppage time at Camp Nou.
The Scottish champion 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 home side leveled the scores shortly before the break, though, when a neat, intricate move involving Xavi and Lionel Messi, Andres Iniesta stabbed the ball into the bottom right corner.
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 a Adriano ball into the box.
Barcelona coach Tito Vilanova rang the changes for the game, bringing in young center back Marc Bartra, Xavi, Adriano, Pedro and Alexis Sanchez for the suspended Sergio Busquets while David Villa, Cesc Fabregas, Martin Montoya and Cristian Tello dropped out of the starting eleven.
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 home side should have taken the lead as early as the second minute when a cute pass in behind the back four from Lionel Messi saw Sanchez miss a one-on-one chance, dinking his effort just past the post.
It was Celtic which took a shock lead in the 17th minute, though, with Mulgrew's viciously whipped free kick from the right wing proving too difficult to handle and Mascherano was left red-faced after nodding into his own net under pressure from Samaras.
After finding itself frustrated for the majority of the half, struggling to break down a stubborn Celtic defense, Barcelona drew level right on the stroke of halftime through Iniesta, who latched on to a magnificent through ball from Xavi to poke the ball past the onrushing Forster.
It was Celtic which managed to create the first chance of the second half, though, when Barcelona's weakness from set pieces was almost cruelly exposed again with the impressive Victor Wanyama planting his header just wide after another superb Mulgrew center.
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 what looked like an offside position just six yards from goal after some good work by both Sanchez and Pedro.
Moments later, it took another save of magnificent quality to keep out a Messi header from point-blank range after Forster launched himself at a delicately clipped ball over the top from Xavi as the game headed into the final 10 minutes.
But Celtic's resolve was broken in the 93rd minute when Adriano's cross into the far post saw Alba steal in ahead of his marker and poke home to hand Barcelona all three points on a night where the visiting side had defended superbly.
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