Yunel Escobar hit a two-run homer off Garrett Richards (2-1) in Toronto's seven-run second inning and Brett Lawrie of Langley, B.C., added some insurance with a three-run shot in the eighth.
Alvarez (5-6) was being closely monitored after leaving last Monday's game in the sixth inning with stiffness in his right elbow. He pitched seven strong innings to win his second game in a row after going winless in his previous seven starts.
"He was able to get loose with no problems after a couple of long innings,” Blue Jays manager John Farrell said. “A very encouraging day in a number ways for Henderson."
An MRI on Tuesday showed only mild inflammation, which was a relief to the Blue Jays considering they recently lost three starting pitchers to injury.
"In light of five days ago, the fact that he was able to go out and pitch extremely efficient, a lot of early outs, his pitch count well in check, he did an outstanding job and really what we needed," Farrell said.
Alvarez held the Angels to seven hits and one run on 80 pitches.
"It’s been a while since a starter has worked deep in the game to give some of our relievers some down time," Farrell said. "And the fact that we built a pretty good cushion early in the game may have reduced some of the stress from some of the pitches Henderson delivered today."
Alvarez had three strikeouts and didn't walk a batter.
“I worked really hard with the sinker,” Alvarez said through translator Luis Rivera. “I was keeping the sinker down. I was using the change-up a lot and didn’t throw one slider today. So it was sinker, change-up.”
Alvarez pitched from the third-base side of the rubber for the second start in a row and it has helped him regain the heavy action on his sinker.
“I think the move to the third-base side has had a lot of effect,” Farrell said.
Richards was charged with 10 runs in 4 1/3 innings but only five were earned as the Angels blundered their way through Toronto's big frame. He allowed nine hits and walked four.
The Blue Jays have been more consistent in recording solid at-bats, fouling off good pitches and working the count.
"I think it’s not worrying about the result," Lawrie said. "I think it's more or less worrying about hitting the ball hard, hitting it on the screws and not worrying about where it goes. Obviously you’ve got to get yourself into good counts to be able to do that."
Farrell has been impressed with the offensive effort over most of the last month.
“It’s been like that for a pretty good stretch here,” Farrell said. “It’s not just been this series, it goes back two or three weeks.”
The Blue Jays (40-38) took the lead in the first inning when Lawrie scored from third on Jose Bautista's double-play grounder.
Lawrie opened the inning by grounding a double past first base. He slid safely into third on a Colby Rasmus grounder to shortstop Andrew Romine, whose throw to third was too late to nab Lawrie.
Johnson opened the second with a double and Escobar hit his fifth homer of the season.
The inning continued when J.P. Arencibia singled, took second on a passed ball and scored when centre-fielder Peter Bourjos dropped Lawrie's fly ball.
"That's probably one of the most difficult times I've had [seeing] balls, especially with balls that didn't get above the stadium and into the sky," Bourjos said.
"If the ball doesn't get up, it's tough to see. If I'm able to make that play (the inning) never happens. That inning snowballed after that play and it didn't get better."
Rasmus doubled to score Lawrie and Bautista singled Rasmus home. Edwin Encarnacion singled to left and Mike Trout's throwing error allowed Bautista to score and Encarnacion to go to third.
Johnson tripled to complete the scoring as Toronto equalled its biggest inning of the season, first done April 15 against Baltimore. It was the largest single-inning outburst against the Angels (43-35) this season.
"We caught a couple of breaks in that second inning that helped contribute to that seven runs," Farrell said.
"You give a team five or six outs and they're going to score seven runs in an inning," Angels manager Mike Scioscia said. "We're going to turn the page. We just got beat up today and we've got to get better tomorrow."
The Angels scored in the third on a single by Bobby Wilson and a double by Maicer Izturis.
Richards walked Adam Lind and Arencibia in the fifth before being replaced by David Carpenter, who was greeted by Lawrie's eighth homer of the season.
Former Angels pitcher David Pauley pitched the ninth for Toronto and gave up three singles with Romine's hit driving in a run.
Notes: Attendance at Rogers Centre was 29,287.... Rasmus made a diving catch before sliding onto the warning track in left centre to rob Albert Pujols of a hit in the eighth inning ... Lawrie had his stretch of reaching base safely ended at 17 consecutive games on Friday when he was 0-for-5. He came back Saturday to go 3-for-4 before being replaced at third by Omar Vizquel. ... Left-hander Aaron Laffey (0-0, 1.80 earned-run average) will start the series finale for Toronto on Sunday against left-hander C.J. Wilson (9-4, 2.36 ERA).