Matt Joyce and Sean Rodriguez added solo shots for Tampa Bay, which had not homered more than twice in any game this season. Joyce homered for the second straight game and got three hits and scored three runs.
Scott hit his third career grand slam and first since 2010 as the Rays broke the game open with a six-run ninth.
David Price (2-1) rebounded from a poor outing at Boston last Friday to improve to 10-2 in 14 career starts against Toronto. The left-hander allowed two runs and eight hits in 5 2-3 innings.
Price is 4-0 in five career starts at Rogers Centre.
Rays reliever Wade Davis worked 1 2-3 innings, Joel Peralta struck out two in the eighth and J.P. Howell finished in the ninth.
Moved up to second in the batting order after starting 10 of the first 11 games in the fifth spot, Zobrist responded with a two-run shot to right in the first inning off Brandon Morrow (0-1).
Zobrist came in 3 for 21 with nine strikeouts in his career against Morrow.
Toronto answered in the bottom half when Yunel Escobar singled and later scored on Jose Bautista's single up the middle.
Joyce led off the second with a double and scored on Rodriguez's sacrifice fly.
Jeff Mathis hit a solo homer in the bottom half, cutting it to 3-2, but the Rays extended their lead in the fourth when Joyce hit a two-out double and Jose Molina singled.
Tampa Bay tacked on two more in the sixth when Joyce hit his third home run and Rodriguez hit his first.
The Rays put it away in the ninth against Carlos Villanueva, who was pitching for the first time since April 8 at Cleveland. Carlos Pena drew a bases-loaded walk, Evan Longoria followed with an RBI single and Scott hit his third homer.
Morrow came in 4-2 with a 2.25 ERA in his six previous starts against the Rays, but was far from effective in this one. He allowed six runs and eight hits in six innings, walked three and matched a career-high by giving up three homers.
NOTES: Escobar matched his career high with four hits, going 4 for 5. All of his hits were singles. It's the ninth four-hit game of his career. ... Toronto GM Alex Anthopoulos said either Double-A RHP Drew Hutchison or Triple-A RHP Jesse Chavez will likely be called up to start at Kansas City on April 21, the next time the Blue Jays need a fifth starter. ... Toronto RHP Henderson Alvarez, who'll face Tampa Bay RHP Jeremy Hellickson in Thursday's series finale, celebrated his 22nd birthday Wednesday.
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