Rogers (4-7) yielded just a second-inning single to Martin Prado en route to the dominating win. The right-hander walked one and struck out five, tossing 53-of-83 pitches for strikes.
Edwin Encarnacion led the Blue Jays' offense with a two-run homer, his 35th clout of the season.
Arizona's Brandon McCarthy (3-9) absorbed a complete-game loss, surrendering four runs on five hits. He didn't issue a walk and struck out two.
Willie Bloomquist got the Diamondbacks' only RBI.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys