Messi then took matters into his own hands from outside the area and thumped the ball off the far post with such venom that it landed just inside the opposite post.
Alaves Luis Rioja pounced on a mistake by Ilaix to reduce the deficit in the second half but Barca came roaring back with a second strike from Trincao, another long-range missile from Messi and then a fifth goal crafted by Messi and Griezmann and finished off by left back Junior Firpo.
A seventh consecutive league win took Barca up to second in the standings on 46 points, eight behind leaders Atletico Madrid who beat Granada 2-1 earlier on Saturday and have a game in hand.
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