Hutchison (6-6) held the Brewers to three hits, struck out a season-best 10 and walked two, picking up his first win since June 13. Aaron Loup, Dustin McGowan and Casey Janssen combined to work the final two innings, with Janssen recording the final three outs for his 13th save of the season.
Ryan Braun drove in the lone run for the Brewers, who have lost two in a row after winning four straight.
Marco Estrada (7-5) started for Milwaukee and suffered the loss, allowing two runs on six hits over six-plus innings of work. He struck out two and walked one, losing for the first time since June 15.
Bautista's first-inning solo homer and Rasmus' solo blast in the fifth gave Toronto a 2-0 lead.
Milwaukee got a run back in the sixth on Braun's two-out RBI double, but wasted a golden opportunity to get more runs in the seventh. With the bases loaded and two outs, Jean Segura flied out to right field to end the inning.