Celta visited Catalonia last month in the league, with the game ending 2-2, and another draw can be backed at 27/4 (7.75).
Roles were reversed on 28 minutes as Messi's angled ball found Alba who sneaked a shot in at the front post.
Messi again showed his special understanding with Jordi Alba by meeting the left-back's low cross first time for the opener in the 13th minute and moments later played a one-two with the Spain worldwide and slammed the ball into the bottom corner.
Messi not only scored two in the first half as Barca eased 4-0 clear at the break at the Camp Nou, but he also played in Jordi Alba for his side's third goal with sublime accuracy.
The Galicians held the Catalans to a 2-2 draw in early December before the 1-1 stalemate in the first leg of this tie.
And three minutes later, Luis Suarez got in on the action by pouncing on a poor back pass.
With the Sky Blues in fine form at the moment, chances are that Ernesto Valverde will field a much stronger side in the return match, although there will be no place for marquee signing Philippe Coutinho, who is out through injury.
Samuel Umtiti took part in Barcelona's training session on Tuesday as the centre-back continues his recovery from a hamstring injury.
Barca did make it a five-star performance, though, as Rakitic took advantage of some woeful Celta defending to head home from a corner three minutes from time.
New £145million signing Coutinho was not named in Barca's squad.
"It's a luxury to have Leo in the side, he's the best in history", he said.