Mike Zunino added a two-run, pinch-hit single in the eighth as the Rays took two of three games in the series and have now won six of their last seven games, all on the road.
The Blue Jays scored once in the first when leadoff batter McKinney doubled and Galvis singled him home.
The Rays answered with an unearned run in the third. Michael Perez singled, Blue Jays second baseman Lourdes Gurriel Jr. threw errantly on Ji-Man Choi's two-out grounder, Avisail Garcia walked and Brandon Lowe hit an RBI single.
Gurriel was replaced at second base by Alen Hanson in the fourth, but the Rays scored two unearned runs in that inning. Kevin Kiermaier reached second base on Stroman's throwing error after a bunt. Willy Adames followed with an infield single, Perez walked, and Austin Meadows and Yandy Diaz each produced RBI groundouts.
Thomas Pannone replaced Stroman in the fifth and struck out the side on nine pitches. He also was perfect in the sixth and seventh.
Toronto left the bases loaded in the fourth and the fifth, Kolarek replacing Morton to get the final out of the fifth. Kolarek retired the first two batters of the sixth before Chaz Roe replaced him and pitched around an Adames error.
Galvis hit his fifth homer this season against Ryne Stanek with one out in the seventh. But after Justin Smoak singled, Diego Castillo induced a double-play grounder to end the inning.
The Rays tacked on five runs in the eighth. Javy Guerra surrendered Garcia's leadoff double and issued a one-out walk to Daniel Robertson. Tim Mayza yielded an RBI double to Kiermaier, Zunino's two-out single and the first homer of the season by Heredia, who batted for Meadows.
Wilmer Font walked Danny Jansen and gave up McKinney's first homer of the season in the ninth.
--Field Level Media