Midfielder Xavi struck after just four minutes as Barca protected their 3-2 advantage from the first leg to clinch a place in the quarter-finals.
Bhoys boss Gordon Strachan opted to leave Jan Vennegoor of Hesselink up front as a lone striker, with leading scorer Scott McDonald surprisingly left on the bench.
However, Strachan's plans went out of the window early on in the Camp Nou, as Lionel Messi, Xavi and Ronaldinho combined to feed Sylvinho and his cross from the left was flicked over Artur Boruc by Xavi.
Barca were then content to sit back and ensure they maintained a two-goal aggregate cushion, although skipper Carles Puyol forced a smart save from Boruc just before the half-hour mark.
Seven minutes before the break the home side were forced to make a change, as Messi had to leave the field with a hamstring problem, but Celtic's joy was short-lived as Thierry Henry entered the fray in place of the Argentinian.
Early in the second half Vennegoor of Hesselink headed wide from Aiden McGeady's accurate cross, after Strachan had brought on Evander Sno at the interval to try and shake things up.
However, Boruc had to be at his best to keep his side in with any chance of causing an upset, as he made top-class saves from Ronaldino and Deco shots from distance.
Samuel Eto'o then passed up a clear chance from close range, as Barca again threatened to add to their tally.
In the closing stages though, Celtic showed their fighting spirit as McDonald forced keeper Victor Valdes into action after coming on for Paul Hartley.
Boruc then blocked an effort from home sub Eidur Gudjohnsen, before Valdes excelled in pushing away a late Shunsuke Nakamura drive as Barca won through with some ease.