The Blue Jays ended a three-game losing streak, one shy of their season high, and won for the third time in 14 meetings with Milwaukee.
The Brewers had their four-game road winning streak end as they lost away from home for just the third time in 13 games.
Starting for the first time since leaving a June 22 game at Cincinnati with a strained left hamstring, Bautista gave the Blue Jays an early lead with a two-out blast off the facing of the second deck in the first inning. The homer was his first since June 6 against St. Louis.
Starting as the designated hitter, Bautista went 1 for 4 with a strikeout. He hopes to return to right field Wednesday.
Rasmus made it 2-0 with a leadoff drive in the fifth.
Both homers came off Milwaukee right-hander Marco Estrada, who has allowed an ML-high 26, nine more than the next highest total.
Estrada (7-5) lost for the first time in three starts, allowing two runs and six hits in six innings. He walked one and struck out two.
Hutchison (6-6) came in 1-4 with an 8.13 ERA in six home starts but delivered his best performance of the season at Rogers Centre. The right-hander allowed one run, three hits and two walks in seven innings.
Hutchison retired the first 14 batters he faced before outfielder Khris Davis reached on an infield single to shortstop in the fifth. Hutchison followed by getting Lyle Overbay to fly out.
Milwaukee cut the deficit in half with a two-out rally in the sixth when Scooter Gennett singled and scored on Ryan Braun's double.
The Brewers loaded the bases with two outs in the seventh thanks to a pair of walks and a hit batter, but Hutchison escaped by getting Jean Segura to fly out.
Aaron Loup started the eighth but left after hitting pinch hitter Rickie Weeks. Dustin McGowan came on and got Braun to ground into a double play. Jonathan Lucroy walked but McGowan fanned Carlos Gomez.
The Blue Jays added two runs in the eighth against reliever Rob Wooten. Melky Cabrera hit an RBI triple and Edwin Encarnacion drove in Cabrera with a double off the wall in center.
Casey Janssen finished for his 13th save in 15 chances.
NOTES: Elian Herrera replaced Davis in left in the seventh. ... Gomez returned after sitting out Sunday's game with a strained neck. Gomez suffered the injury in an outfield collision with Ryan Braun Saturday. ... Segura returned for Milwaukee after missing Sunday's game with a sore left quadriceps. ... The Blue Jays wore special red caps and jerseys to mark the Canada Day holiday. ... Attendance was 45,088, Toronto's sixth sellout of the season. ... Canadian IndyCar driver James Hinchliffe threw out the first pitch. ... Brewers RH Wily Peralta (9-5) faces Blue Jays LH J.A. Happ (7-4) on Wednesday.