The result extended Barcelona's unbeaten streak to 21 matches in all competitions.
They have not lost in the league since November a year ago, when they fell 4-3 to Real Betis Balompie at home.
Alaves were dealt a blow when they lost Diego Rolan on the stroke of half-time, with Darko Brasanac replacing him for the start of the second half.
Michel scored the victor with a shot from outside the area in the 67th minute, ending his team's five-match winless streak.
Tuesday's two remaining matches were significant in the battle against relegation with Huesca giving themselves a slim chance of survival and climbing off the bottom of the table with a 2-0 win at home to Eibar.
On Sunday, Real Madrid make the short trip to struggling Rayo Vallecano, while Getafe visit Real Sociedad in their bid to secure a top-four finish for the first time.