Alvarez became the second Toronto pitcher in as many nights to shut out the Angels, who have gone 22 consecutive innings without scoring a run. Alvarez limited the Angels to six hits one night after Brandon Morrow allowed Los Angeles just three hits Thursday.
It was the fourth straight shutout produced in the Angels' ball park. Los Angeles blanked Minnesota both Tuesday and Wednesday, with the second of those shutouts being the no-hitter thrown by Jered Weaver.
Alvarez (2-2) struck out three with a walk while throwing just 96 pitches. He gave up a leadoff double in the ninth, but was allowed to stay in the game and he retired the next three batters.
It was the Blue Jays' fourth straight win.
Toronto took the lead with a three-run third, two of the runs scoring on a homer by Jose Bautista.
That blast came off starting pitcher Ervin Santana, who has lost all of his six decisions this year. He gave up three runs on just three hits with 10 strikeouts in eight innings.