Manager John Gibbons said Hutchison had "a dynamite fastball."
"When he's on, he's on," Gibbons said.
Pitching on an extra day's rest, 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.
"The ball riding up a little bit with that extra life kind of caught us off guard," Overbay said. "It wasn't in the scouting report."
However, the Brewers did get a late scouting report from leadoff batter Scooter Gennett, who lined out to begin the game and brought a warning back to the bench.
"He came back and said `Hey, when his ball is up, it takes off," Overbay said. "It kind of looks good coming in so you end up swinging at it anyway."
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.
"I was able to make good pitches and get ahead," Hutchison said. "That has a lot to do with it."
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, much to the delight of a Canada Day crowd of 45,088.
"It's Canada Day in front of a nice crowd," Gibbons said. "You don't want to lay an egg."
The Brewers had their four-game road winning streak end as they lost away from home for just the third time in 13 games.
"We didn't get a lot of hits," manager Ron Roenicke said. "A lot of strikeouts, not a lot of hits."
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 in the first. The homer was his first since June 6 against St. Louis.
"Obviously, adding a guy like Bautista helps," Brewers right-hander Marco Estrada said. "He's one of the better hitters in the game."
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 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.
Milwaukee cut the deficit in half with a two-out rally in the sixth when 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.
Casey Janssen finished for his 13th save in 15 chances.
Elian Herrera replaced Davis in left in the seventh after Davis suffered a strained pectoral muscle sliding into second base. Davis said the injury was "mild." ... 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. ... 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.