Messi netted once in either half on his return to the team as the Spanish champions secured all the points to advance into the round of 16 as winners of Group C. Meanwhile, Celtic's European journey is now over ahead of their final group match away to Manchester City next month.
Celtic boss Brendan Rodgers recalled Jozo Simunovic, Tom Rogic and Emilio Izaguirre to his starting XI for the clash in Scotland, while it was once again Scott Sinclair in support of leading scorer Moussa Dembele in the final third.
As for Barcelona, Messi and Luis Suarez both returned after missing the 0-0 draw with Malaga at the weekend, while Jordi Alba and Andre Gomes were also included in arguably Luis Enrique's strongest available team.
Sinclair's explosive pace in a wide position caused Barcelona all sorts of problems in the opening 10 minutes and Javier Mascherano had to be alert to prevent Dembele from having a free header after a very bright start from the home team.
Barcelona's first sight of goal arrived when Neymar's flick set Messi free inside the Celtic box, but the Argentine's goal-bound strike was blocked, before the skipper failed to control a delicious Sergio Busquets pass as Celtic survived a couple of dangerous moments in quick succession.
Messi again came close in the 16th minute after combining with Alba down the left, but the attacker swept his low effort wide of the post, minutes before failing to make contact on an Ivan Rakitic header, which dropped kindly inside the Celtic box.
The pressure continued to build and eventually Barcelona made the breakthrough in the 26th minute of action when Neymar delivered a stunning pass in to Messi, who beat Craig Gordon at his near post with a clever finish to temporarily silence the home supporters at Celtic Park.
It did not take long for normal service to resume in terms of the blistering atmosphere, but Celtic were struggling to contain a dominant Barcelona team, who knew that all three points would ensure that they booked their spot in the knockout stage of the competition with one game to spare.
Dembele proved to be Celtic's main threat in the first period and the Frenchman brought a smart save from Marc-Andre ter Stegen in the 37th minute, before Gordon made an even better stop down the other end - keeping out a Suarez header from point-blank range to prevent the hosts from conceding a second goal.
Celtic were forced into a change at the interval, with Sinclair unable to continue after a late challenge from Alba, which allowed James Forrest to come into the action as the hosts looked for more cutting edge in the final third of the field.
Rodgers's side had the first clear chance of the second period after Callum McGregor worked a yard of space outside the Barcelona box, but the midfielder just hesitated at the final moment and his shot towards the bottom corner was always comfortable for Ter Stegen in the away side's net.
Celtic had their best chance of the match in the 53rd minute when Forrest delivered a stunning cross onto the head of Dembele, who had pulled clear of the Barcelona defence, but the French youngster could only angle his effort straight into the arms of Ter Stegen.
Less than two minutes after that Dembele chance, Barcelona scored their second of the night as Messi converted from the penalty spot after Izaguirre had clumsily brought Suarez to the ground with a late challenge.
Dembele remained Celtic's main danger and headed over the crossbar in the 64th minute, before Messi just missed the post down the other end after Neymar had once again dazzled the Celtic backline with his ability to change direction at any given moment.
Neymar did not endear himself to the home supporters in the latter stages, however, and the Brazilian, who had a long-running feud with Mikael Lustig, left the field to a chorus of boos in the 77th minute of action.
Suarez had a golden chance to add his name to the scoresheet in the 84th minute after a smart pass from Messi found the Uruguay international, but he clipped the outside of the post as it remained 2-0 on the night.
Borussia Monchengladbach's home draw with Man City means that Celtic will finish bottom of Group C regardless of what happens in their final match away to also-qualified Man City next month, while Barcelona have secured top spot ahead of their last game at home to Gladbach.body check tags ::