PSG host relegation battling Le Havre on Saturday
Teenage forward Ansu Fati put Barca in front midway through the first half after the visitors had hit the woodwork three times, while Messi and strike partner Luis Suarez further stretched their lead before halftime.
Barca finished the season second in the standings on 82 points, four behind champions Real Madrid who visit Leganes later on Sunday. Alaves are 16th on 39.