Bautista hit an RBI double in the first inning and added a leadoff homer in the seventh, his first since July 2.
David Ortiz hit a three-run homer for the Red Sox, his fourth in three games, but Boston lost its second straight after winning the previous five.
Dickey (8-10) allowed four runs and nine hits in six innings, walked one and struck out five.
Rookie Aaron Sanchez, selected from Triple-A Buffalo on Tuesday, made his debut with two perfect innings and Casey Janssen finished for his 15th save in 17 chances.
The Red Sox went up 3-0 before Dickey could record an out. After Shane Victorino and Dustin Pedroia singled to start the game, Ortiz followed with a towering drive off the facing of the fourth deck. The homer was his 455th, tying him with Adam Dunn of the Chicago White Sox for 35th on the career list.
Ortiz’s drive was his 37th at Rogers Centre, breaking a tie with Alex Rodriguez for the most by a visiting player.
Ortiz, who went deep in consecutive at-bats Monday and connected again Tuesday, homered in three straight games for the first time since June 17-20, 2012.
The three RBIs gave Ortiz 1,501 for his career, making him the 53rd player in major league history with 1,500 or more.
Staked to an early lead, Red Sox right-hander Clay Buchholz couldn’t make it stand up for long. Jose Reyes singled and Melky Cabrera walked to begin the bottom of the first before Bautista hit an RBI double.
Bautista scored on a grounder and Josh Thole hit an RBI double over the head of Daniel Nava in left.
Boston reclaimed the lead with consecutive doubles by Nava and Xander Bogaerts in the fifth, but Toronto answered with two runs off Buchholz in the sixth.
Thole walked and scored on Ryan Goins’ first career triple. Two batters later, Goins scored on a throwing error by shortstop Bogaerts.
Bautista made it 6-4 with a first-pitch homer off Andrew Miller in the seventh that bounced off the top of the wall and out.
Buchholz (5-6) lost for the first time in three starts, allowing five runs, four earned, and six hits in six innings.
He walked four and struck out one.
NOTES: Pedroia’s first-inning single snapped an 0-for-17 slump. … Red Sox rookie INF-OF Brock Holt did not start for the first time in 59 games. Holt had played an AL-high 533 innings since his streak began May 17. … Boston RHP Rubby De La Rosa (3-2) faces RHP Marcus Stroman (5-2) in Thursday’s series finale.
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