Messi, who missed Saturday's goalless draw with Malaga due to illness, provided a fine finish to Neymar?s lofted pass to hand his side a 24th-minute lead.
Messi, who missed Saturday's goalless draw with Malaga due to illness, provided a fine finish to Neymar's lofted pass to hand his side a 24th-minute lead in Glasgow.
The Barcelona captain, who grabbed a hat-trick in the 7-0 mauling in the reverse fixture at the Camp Nou, then converted a 56th-minute penalty won by Luis Suarez to see his side top Group C with 12 points from five games.
Manchester City's draw with Borussia Monchengladbach in the group's other match also sent the English side through, with Celtic condemned to a last-place finish behind the Germans.
Apart from the injured Andres Iniesta, Barcelona named their strongest 11 as Suarez and Messi returned from suspension and sickness respectively to form their formidable partnership with Neymar in the Barca attack.
Both manager and captain had urged Celtic to be brave against the side that had served such a crushing defeat to them in Spain. Certainly Celtic didn?t allow the visitors time to dwell on the ball as they pressed high up the pitch early on. However, Barcelona began to probe at the Celtic defence with Mikael Lustig looking particularly vulnerable to the runs of Jordi Alba and Neymar.
The Brazilian was first to burst into the Celtic box and teed up Messi with a backheel and the Argentine?s deflected shot had Craig Gordon scrambling across his line before it was cleared.
Alba was then the provider as his cross from the left found Ivan Rakitic lurking in the box but the Croatian international sent his header bouncing into the turf and over the bar.
Celtic failed to heed the warning signs and Barca soon had a deserved lead through Messi. Neymar -- who learned earlier in the day that Spanish prosecutors were seeking a two-year jail sentence and a 10-million-euro ($10.6 million) fine for his part in his allegedly fraudulent transfer to the club -- was given space to play a wonderful lofted pass to Messi, who crashed a sublime shot on the half-volley in off the near post.
The hosts tried to respond and had their first shot on target in the 37th minute when Moussa Dembele stung the palms of Ter Stegen with a fierce strike.
Only a superb save from Craig Gordon stopped Suarez from adding a second before the break as he blocked a point blank header from the Uruguayan international with his body.
Celtic lost Sinclair to injury at the break but his replacement - James Forrest - created Celtic?s best opportunity when he picked out Dembele with a cross from the left but the in-form French forward sent a tame header straight to Marc-Andre ter Stegen.
It was to prove costly as Barcelona doubled their advantage moments later. Suarez got on the wrong side of Emilio Izaguirre and the Celtic defender hauled him to the ground to earn a penalty that Messi sent straight down the middle to score his 92nd Champions League goal for the Catalan giants.
Neymar was fortunate, though, to escape with just a booking, which will see him miss the final group game, as he pushed Lustig to the turf after the players had clashed, with the Brazilian international subbed moments later.