Barcelona made no mistake in accounting for the other half of Glasgow's Old Firm, having beaten Rangers earlier in the same competition.
Celtic needed their first Champions League away victory in order to progress after losing the first leg 3-2 in Glasgow.
Scott McDonald, the Glasgow club's top scorer, was the surprise omission as manager Gordon Strachan opted for a conservative formation, with Jan Vennegoor of Hesselink in a lone striker role while Paul Hartley came into in a five-man midfield.
Mark Wilson, recently recovered from a knee operation, replaced cup-tied right-back Andreas Hinkel for his first start since last September.
Lionel Messi returned to the Barca line-up after starting on the bench for the 4-2 La Liga defeat by Atletico Madrid at the weekend.
However, all of Strachan's good pre-match intentions were ripped up, when Barca, full of verve, caught Celtic cold to open the scoring.
Messi, driving forward, found Xavi who played in Ronaldinho, who, in turn, cleverly brought in Silvinho on the overlap.
The Brazilian defender clipped in an inviting cross, and with the Celtic defence hesitating, Xavi flicked out a boot to guide the ball over Boruc and into the net.
Celtic's Shunsuke Nakamura is challenged by Deco
With the Scots falling victim to a quickfire blow, it was a portent of things to come, with Barcelona displaying their customary class and one-touch football.
Despite Barcelona enjoying the bulk of the initial play, Celtic managed to recover from Xavi's early strike.
Boruc did rescue his team-mates from conceding a second in the 27th minute, though, with an alert tip over the crossbar from a lob by the unlikely figure of Carles Puyol.
Messi had to leave the field with a hamstring injury shortly afterwards, to be replaced by Thierry Henry.
Barcelona demonstrated their quality in possession but, as the first half came to it's conclusion, they did not carve out the expected host of opportunities, much to the relief of their opponents.
Massimo Donati was replaced by Evander Sno at half-time as Celtic slowly began to improve.
Vennegoor of Hesselink should have done better with a glancing header from Aiden McGeady's inviting cross, before Giorgios Samaras came on for the Dutchman.
Barcelona eased into their stride again, forcing Boruc to make two excellent saves in succession, the Pole firstly stopping Ronaldinho's thunderous shot from 18 yards before scooping away a raking Deco effort.
Samuel Eto'o found himself unmarked in the six-yard area but the striker showed uncharacteristic hestitancy and his chance was gone.
Eto'o was in threatening mood in the closing stages, but Celtic, to their credit, were defending well.
Valdes was tested by substitute McDonald in the final minutes but it was, in truth, a rare moment of concern for the Barcelona keeper.
Boruc stood firm to deny Eidur Gudjohnsen, before Nakamura's long-range strike brought out a good late stop from Valdes.
And denied an equaliser on the night, Celtic exited Europe's premier competition at the same stage for the second successive season.
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