Xavi scored the only goal in the opening moments as Barcelona moved into the quarter finals, but
Lionel Messi tore his hamstring to take the gloss off the victory.
After winning the first leg two weeks ago, the Blaugrana were expected to progress and after taking the lead on the night early on the outcome was a formality.
While Barça were never in top form, Víctor Valdés only had saves to make in the closing minutes as Celtic placed the emphasis on defence for long periods.
Messi's injury will cause concern as the Argentinian limped out of the action in tears after pulling up and it is bad news for the Catalan outfit.
Celtic manager Gordon Strachan said before the game that his side need a miracle and that was certainly the case after just three minutes.
Xavi began the move as he rolled the ball to Ronaldinho, who in turn found Sylvinho and his cross was converted superbly by Xavi as he clipped the ball over Artur Boruc in the visitors' goal.
It was just the start that Frank Rijkaard would have wanted after the league defeat at the weekend by Atlético, but it proved to be the only goal of the game.
The hosts certainly had plenty of chances as Ronaldinho looked to be enjoying himself, while Eto'o was always busy.
It was those two that had chances soon after the goal as Eto'o chested a cross just wide and Ronaldinho saw a drive too powerful for Boruc to catch, bt the keeper did keep it out.
On the half-hour mark, Carles Puyol of all people ventured forward and was picked out in the area, but his flicked shot was tipped over by Celtic's custodian.
Five minutes later and Barça's night was spoiled as Messi pulled up in mid-run and appeared to know immediately that something was seriously wrong.
After lying down holding the back of his leg, the forward was walked off the pitch while several teammates consoled him.
The news that he has torn a hamstring will have an affect on the next few weeks as pundits and fans had clamoured for Messi's inclusion after he was left on the bench at the weekend.
Henry came on to replace the Argentinian, but there were no more clear chances before a half-time break that Strachan reportedly used to make it clear he was not happy with his team.
Celtic did raise their game at the start of the second period as they closed down Barça quicker and stopped giving the ball away as cheaply as they had been.
Just before the hour mark, Eto'o flicked the ball over to Ronaldinho and the Brazilian hammered a half-volley at goal which produced a fine save from Boruc.
Soon after Zambrotta sent the ball into the area where Eto'o just failed to steer it on target after beating the Celtic offside trap.
AS full time approached Valdés was forced to make his first two saves as Scott McDonald took aim with a low drive and Shunsuke Nakamura did even better with a fine drive.
goal.com