Alba's goal ensured a 2-1 win and means Barca have a 100 percent record in the group they share with Celtic as well as Benfica and Spartak Moscow.

Barca coach Tito Vilanova finally decided to give young central defender Marc Bartra his first game of the season, while Adriano switched to play at right back instead of Martin Montoya.

Meanwhile Alex Song returned to central midfield to cover for the suspended Sergio Busquets.

Celtic meanwhile had traveled with four points from two Champions League matches and were cheered on by an estimated 5,000 fans. Celtic coach Neil Lennon included Greek striker George Samaras in his side along with Gary Hooper.

Barca sent the first warning as Alexis Sanchez fired wide from close range, but Celtic opened the scoring from a set piece. Samaras won a header and the ball took a deflection on its way past Barca keeper Victor Valdes.

That was the sign for the home side to take virtual control of the ball, but against a well-organized defense that was happy to sit on the edge of their penalty area, chances were few and far between until Andres Iniesta scored the equalizer following a swift exchange of passes with Leo Messi in the final minute of the half, just after Samaras had to leave the pitch with an ankle injury.

The second half began in the same way, with Barca in control, but struggling to carve out chances and struggling every time they had to defend a set piece. Victor Wanyama was close to heading Celtic ahead 10 minutes into the second half. Barca had over 70 percent of possession and Messi saw a fine chance saved when Fraser Forster produced a point blank save, although as the game opened up, Celtic also looked dangerous thanks mainly to substitute Kris Commons down the right flank.

Forster then made another flying save from a Messi header after Andres Iniesta had tried an audacious chip, just before Christian Tello replaced Pedro Rodriguez for Barca.

The last 10 minutes were a Barca monologue but there was simply no space for Barca to move the ball in or on the edge of the Celtic area, where the entire visiting side was camped out defending bravely.

David Villa hit the post in the last minute after passes from Messi and Iniesta and that looked as if it was the last chance but Jordi Alba popped up in the final seconds to score a dramatic winning goal that Barca deserved for their efforts, but which was cruel on a Celtic side that had performed with order and courage.