Michael Young, once a Minor Leaguer with the Blue Jays, had three hits, including a three-run homer, and five RBIs.
The winning pitcher was left-hander Matt Harrison (14-7), who held the Blue Jays to two hits and two runs -- one on Mike McCoy's first homer of the season -- over eight innings. He offered his condolences for Alvarez when he was told.
"I'll say a little prayer for his family and him tonight," Harrison said. "That's pretty tough. To have that on your mind when you go out and pitch, your focus is definitely not on pitching. I hope the best for him, hopefully he can get past this and come back strong."
"I had absolutely no idea," said Yan Gomes, who caught Alvarez on Sunday when asked if he knew.
Manager John Farrell made no reference to it in his postgame news conference.
The loss before 35,701 at Rogers Centre ended a 10-game homestand for the Blue Jays, who finished it 3-7 even though they won the first game in two of the three series.
"The Rangers came out and swung the bats aggressively, particularly on first-pitch fastballs, and then in hitter's counts where there were some mislocated fastballs, they squared a number of pitches up today," Farrell said. "I didn't think he used his secondary stuff enough, particularly as they started to be aggressive early in the counts. There was still a first-pitch fastball approach that they took advantage of."
"I guess we should have tried to do something else, because what we were doing wasn't working," Gomes said. "It's a team you can't make mistakes against, one through nine they can hurt you."
Alvarez helped himself out of potential trouble with double plays in each of the first two innings and the Blue Jays gave him an early lead.
The Blue Jays (56-65) scored a run in the second after Yunel Escobar led off with a single and Moises Sierra walked. Jeff Mathis, used as the designated hitter Sunday, sacrificed them to second and third. McCoy's groundout to third scored Escobar.
The Rangers (70-50) came back with two runs in the top of the third. David Murphy led off with a double to center and slid safely home on a single to right by Geovany Soto, who took second on the throw home.
Mitch Moreland singled to make it 2-1, and he took third when Ian Kinsler ended an 0-for-21 drought with a double. But Alvarez stopped the Rangers by striking out Elvis Andrus and Josh Hamilton and coaxing a grounder from Adrian Beltre.
The Rangers struck again in the fourth to take a 3-1 lead. Young singled with one out and scored on a double by Murphy, who was thrown out trying for third.
The game unraveled for Alvarez in the fifth. Andrus singled with one out and scored on Hamilton's double. Beltre walked and Nelson Cruz singled to score Hamilton before Young belted his three-run homer.
"It was tough, we kind of let it get away from us a little bit," Gomes said.
"It was good to have a good offensive game as a team," Young said. "We haven't had one of those games in a while, so it definitely felt good. We really fed off [Harrison] today. Usually when you have a good offensive performance, you feed off the starting pitcher."
McCoy hit his first homer of the season in the fifth, but Young doubled home two more runs in the sixth against Brad Lincoln.
Murphy hit his 11th homer of the season in the ninth inning against Chad Jenkins.
First baseman David Cooper was a late scratch from the game with back spasms after batting practice.
"It happened during batting practice," Cooper said. "Nothing major. I'll probably be back in there Tuesday."
After the game, the Blue Jays announced that Gomes was being optioned back to Triple-A Las Vegas. A move will be announced Tuesday, likely the addition of catcher Yorvit Torrealba, who completed a four-game stint with Double-A New Hampshire on Sunday after signing a Minor League contract last week.