Barcelona displayed their class to end Celtic's formidable home European record with a deserved win in Glasgow.
Lionel Messi (right) celebrates with Ronaldinho at Celtic Park
Jan Vennegoor of Hesselink put Celtic in front in 15 minutes with a powerful header only for Lionel Messi to clip home an equaliser three minutes later.
Barry Robson burst forward to loop a header over Victor Valdes to give battling Celtic an interval lead.
Barca levelled through Thierry Henry, before dominating the second half, and Messi tucked in a 79th minute winner.
Celtic - who had won their last three Champions League home matches - included Paul Caddis and Robson for their Champions League debuts.
Caddis appeared in place of the cup-tied Andreas Hinkel, while Robson replaced the suspended Scott Brown in midfield.
Paul Hartley was also included in the starting line-up at the expense of Massimo Donati.
Ronaldinho and Messi both started for Barcelona and Samuel Eto'o was named among the substitutes.
The Catalan giants, the last side to have defeated Celtic in Glasgow on European duty with a 2004 Champions League win, started with plenty of confidence.
And Boruc was quickly called into question with a smart save from an Andres Iniesta volley, before Caddis headed a goalbound Henry drive clear.
Jan Vennegoor of Hesselink headed Celtic in front
Yet, it was Gordon Strachan's men who went in front with their first real raid.
Scott McDonald did well initially to hold the ball up in the penalty area, with Naylor then swinging in a perfect ball, finding Hesselink to power home a header.
It was, indeed, a timely way for the Dutchman to end a run of 15 European games without scoring.
The elation for the home fans didn't last, however, with the Spaniards responding in the right fashion, crafting a superbly-worked leveller.
Messi managed to elude Naylor on the edge of the area, and, upon receiving a perfectly weighted return from Deco, the Argentine instantly fired into the roof of the net for his fifth goal of the tournament.
In the 22nd minute Ronaldinho flighted a free-kick just over the bar as Celtic felt the force of Barcelona's pressing game.
Celtic had due cause to feel fortunate for their Hesselink's opener, but nevertheless, Henry could only squander an opportunity for Frank Rijkaard's men by blasting over the bar.
The Hoops showed a determination to resist being swamped and, once more, surged into the lead, with McGeady the orchestrator.
The Republic of Ireland international cut inside and his cross found Robson, with the midfielder timing his run perfectly into the danger zone to head over the exposed Victor Valdes.
Thierry Henry scored a superb goal for Barcelona
With McGeady dangerous, it was a rather wasteful Barcelona who trooped off at the break.
If the hosts were expecting an urgent repsonse from Barca in the second half, their fears were well-founded, when Henry took centre stage.
With Gary Caldwell losing possession midway inside his own half, Ronaldinho slipped the ball through to the pacy Frenchman, who had time to tee up a right foot effort which effortlessly eluded Boruc to find the top corner.
Giorgios Samaras replaced Hesselink and Mark Wilson came on for Caddis, as Celtic attempted to regain the initiative.
And with Barcelona showing more of their customary verve, Henry slipped the ball just past the post in the 62nd minute.
Valdes denied Donati - a replacement for Hartley - in a rare Celtic threat as the game wore on.
Barca's ominous strength in depth was illustrated when Eto'o replaced Ronaldinho.
A 74th-minute Puyol header was gathered by Boruc with the visitors dominant - and it was no surprise when Messi made his second and Barcelona's third.
With the Celtic defence failing to clear a loose ball, Messi outfoxed Caldwell with a drag-back to guide the ball into the net, leaving Boruc helpless.
The Scots simply could not display their usual fluency as they chased an unlikely equaliser in the closing stages.
Barcelona will now welcome Celtic for the return hot favourties to progress to the quarter-finals, courtesy of the clinical Messi.
Celtic: Boruc, Caddis (Wilson 61), Caldwell, McManus, Naylor, Nakamura, Hartley (Donati 65), Robson, McGeady, Vennegoor of Hesselink (Samaras 55), McDonald. Subs Not Used: Mark Brown, Sno, Killen, O'Dea.
Booked: Hartley, Samaras.
Goals: Vennegoor of Hesselink 15, Robson 38.
Barcelona: Valdes, Puyol, Milito, Marquez, Abidal, Iniesta, Toure Yaya, Deco (Xavi 65), Messi, Henry (Gudjohnsen 88), Ronaldinho (Eto'o 73). Subs Not Used: Pinto, Sylvinho, Giovanni, Thuram.
Booked: Messi, Deco.
Goals: Messi 18, Henry 52, Messi 79.
Ref: Peter Frojdfeldt (Sweden).