Celtic had led at the famous stadium when, in the 18th minute, Georgios Samaras’ header from a Charlie Mulgrew free-kick went in off the back of Barcelona centre-back Javier Mascherano.
And it looked for a while like the Greek striker, who had scored the winner against Spartak Moscow earlier in the month to clinch Celtic’s first away victory in the competition, might have just have played his part in an even more momentous goal.
However, a minute before the break Barcelona midfielder Andres Iniesta levelled, and with the four minutes of injury time almost played at the end of an exhausting evening, defender Alba sneaked in at the back post to slide in an Adriano cross.
However they may have felt, the Celtic players were applauded off by their supporters and manager Neil Lennon would surely have been proud with his side’s spirited performance.
Fraser Forster was in outstanding form, especially in the second half as he made a series of saves to show just why he had been included in Roy Hodgson’s England squad for the World Cup qualifiers against San Marino and Poland.
Moreover, with Spartak beating Benfica 2-1 in Moscow, the Hoops remain in second place with four points from three games as they await the visit of Barcelona to Glasgow for the return game in a fortnight.
Samaras, skipper Scott Brown, Mikael Lustig and Emilio Izaguirre returned to the Celtic side while Kris Commons and James Forrest recovered from respective hamstring and groin injuries which kept them out of the win over St Mirren in Paisley on Saturday to take their place on the bench.
Injured Barca centre-back Gerard Pique joined Carles Puyol, Dani Alves and Eric Abidal on the sidelines and Sergio Busquets was suspended.
Coach Tito Vilanova gave 21-year-old Marc Bartra his first game of the season alongside midfielder Mascherano in central defence, while Argentinian superstar Lionel Messi went into the match on the back of a hat-trick in Saturday’s 5-4 win over Deportivo La Coruna.
Celtic should have gone behind in the second minute when Iniesta split the Hoops defence open with a sublime pass to find Alexis Sanchez but his shot sped past the far post.
The home side, as expected, had the vast bulk of possession but were far from purposeful.
Their next opening did not come until the ninth minute when left-back Alba got in behind the Celtic defence but Izaguirre did well to prevent Pedro getting on the end of the cross.
It seemed like a matter of time before Barcelona, although more methodical than magical, would get the breakthrough.
However, the first half turned on its head within a minute. Forster pulled off a great save from Bartra’s close-range header after the rookie defender had got on the end of an Iniesta cut-back following more prompting by Messi.
The Scottish champions took immediate advantage of their good fortune when Sanchez conceded a free-kick for a foul on Brown wide on the right. Mulgrew’s whipped-in free-kick was met by the head of Samaras and the ball came off the challenging Mascherano and went past the helpless Victor Valdes.
The several thousand Hoops fans high up in the stands could hardly believe what they had witnessed.
Barcelona were stung into action and Messi curled a free-kick over the bar after Brown had fouled him 30 yards from goal.
Moments later, Bartra should have done better from Iniesta’s perfectly-weighted cross from the left but failed to connect properly with his header and the ball went wide.
In the 32nd minute, with the Celtic defence pinned back, Forster made a decent save from right-back Adriano’s long-distance drive.
The home side looked suspect when Celtic attacked but in the 37th minute Messi, after being fouled by Wilson, went close once more with another free-kick from distance which just cleared the bar.
Two minutes from the break Samaras was replaced by Forrest after going over on his ankle.
A minute later Barcelona were level when Iniesta, after taking a Messi pass, worked a one-two with skipper Xavi Hernandez before sliding the ball past Forster from 12 yards as he slid to the ground.
It was a sickener for Lennon’s side who had worked so diligently.
Barcelona dominated possession at the start of the second half although they had a lucky escape in the 53rd minute when Mulgrew’s corner from the right came off Victor Wanyama at the back post with the ball skipping only a yard past the post.
Commons came on for the struggling Brown in the 63rd minute but Barcelona continued to beat a relentless path towards the Celtic goal.
Forster thwarted Messi and Iniesta as the pressure intensified.
In the 68th minute the Englishman made a terrific point-blank save from Messi after the Argentina ace was set up by Adriano.
As Barcelona camped at the edge of the Celtic box, and the defending became more desperate, Forster made further fine saves from Sanchez and Messi.
Barcelona substitute David Villa, on for Alexis Sanchez, crashed a drive off the base of the post but just when it looked like Celtic would hold out, Alba popped up with the winner to break Hoops hearts.