Messi, who missed the goalless draw with Malaga on Saturday with a sickness bug, was back to his tormenting best just as he had been when scoring a hat-trick in Barca's 7-0 win in the their Group C fixture at the Nou Camp two months earlier.
The Argentinian followed up an impressive first-half strike from close range with a penalty after the break, and was a constant threat throughout the match alongside Brazilian team mate Neymar.
The brace took Messi's Champions League total to 92 goals, including nine in this season's group stages alone, and though he narrowly missed a hat-trick, his genius ensured Celtic exited all European competition while Barca will progress as group winners.
"It was a game that we expected. In one of the toughest groups, we have come top. I have to congratulate the team," said Barcelona coach Luis Enrique.
Celtic coach Brendan Rodgers had impressed upon his players not to give their illustrious opponents too much respect as they had done in Barcelona and they were certainly not humiliated in the same manner as they were in September.
They had some decent goalscoring opportunities which fell to striker Moussa Dembele, but he failed to add to his three goals in this season's group stage.
For all Celtic's pressing and possession, however, Barca had too much class with Messi their executioner again, latching on to Neymar's dinked through ball to fire first-time past Craig Gordon in the 24th minute.
He doubled his tally from the penalty spot in the 56th after Luis Suarez was fouled by Emilio Izaguirre.
Messi had further opportunities to add to his tally and only a remarkable save by Gordon from a Suarez header in the first half prevented the winning margin from being wider.
"The players gave everything," said Celtic boss Brendan Rodgers.
"We restricted them to one or two chances and at 1-0 we had a real chance to equalise. However, they went up to the other end and scored a second."
(Editing by Toby Davis)
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