The Argentinian, who scored a hat-trick in the 7-0 home win over the Hoops in the opening Group C fixture, struck from close range in the 23rd minute and doubled his tally from the spot 10 minutes after the break.
Brendan Rodgers’ side put up a better show than they did in the Nou Camp but remain bottom of the section with two points and travel to Manchester City next month for the final fixture unable to finish third for a Europa League spot.
Despite all the home side’s effort, it was a mostly comfortable win for Luis Enrique’s side who qualify for the knockout stages as group winners.
Celtic fans turned up in the hope of a repeat of the 2-1 win over Barcelona four years ago, rather than in any expectation.
Barcelona, though, travelled to Glasgow carrying their worst start to a LaLiga campaign in a decade but they were boosted by the return of Messi after he recovered from illness.
Fellow forward Luis Suarez was back from suspension while Gerard Pique shrugged off a knock to take his place in the defence.
Celtic defenders Jozo Simunovic and Emilio Izaguirre and midfielder Tom Rogic were back in the side but striker Leigh Griffiths failed a fitness test on a tight hamstring.
Barcelona showed early flashes of their class and in the 10th minute Messi failed to control a wonderful through-ball from Sergio Busquets when he would have had only goalkeeper Craig Gordon to beat.
Brazilian forward Neymar was arguably the outstanding Barcelona player on show, conducting play from wide on the left and his little dink found Messi who steered it past Gordon at his near post.
It was a clinical finish, but to their credit Celtic came fighting back and there remained the suggestion that they could fashion an opportunity.
That chance came in the 36th minute when striker Moussa Dembele tested Marc-Andre ter Stegen with a decent drive from 16 yards, the goalkeeper gathering at the second attempt.
However, the visitors retained their potency going forward and it would have been 2-0 had Gordon not made a remarkable save from Suarez’s point-blank header after Messi had reached the byline with a trademark burst of speed.
Winger James Forrest replaced Scott Sinclair at the start of the second half and seven minutes later he planted a cross right on to the head of Demebele but the France Under-21 striker’s header, like Callum McGregor’s drive moments earlier, lacked power.
Celtic paid for that glaring miss almost immediately when Izaguirre’s challenge on Suarez inside the box at the other end saw Italian referee Daniele Orsato point to the spot, with Messi confidently beating Gordon with his penalty.
The home fans did their best to rally their heroes but it was with defiance rather than conviction, and a hush went around the stadium when Messi made a yard of space before screwing the ball wide of the far post.
The Parkhead side kept pushing forward but the Catalans were largely in control - Suarez missed a sitter in front of goal after being set up by Messi - and saw the game out to take their place, inevitably, in the knockout stages again.
Gordon, Lustig, Simunovic, Sviatchenko, Izaguirre, McGregor (Roberts 71), Armstrong, Brown, Sinclair (Forrest 46), Rogic (Bitton 64), Dembele.
De Vries, Toure, Gamboa, Henderson.
ter Stegen, Sergi Roberto, Mascherano, Pique (Marlon 72), Jordi Alba (Digne 65), Rakitic, Busquets, Andre Gomes, Messi, Luis Suarez, Neymar (Turan 76).
Cillessen, Denis Suarez, Rafinha, Alcacer.
Daniele Orsato (Italy).