Giambi's RBI single gave Cleveland the lead in the second.
Cleveland traded Rogers, who was making his eighth start of the season, to Toronto for infielder Mike Aviles and catcher Yan Gomes in November. Rogers struck out seven and held Cleveland to four hits.
Masterson didn't allow a hit until Rasmus led off the fifth with a double. Masterson was coming off his shortest start of the season when he allowed six runs in 4 2-3 innings in a 7-0 loss to Detroit on Friday. He threw a six-hit shutout in his start before against the Chicago White Sox.
Cabrera broke an 0-for-20 slump with a single in the first. Indians reliever Preston Guilmet made his major-leage debut in the seventh and retired both batters he faced.
NOTES: RHP Danny Salazar will be called up from Triple-A Columbus to make his major league debut Thursday against Toronto. "It was a shock when they told me. I didn't know what to say," said Salazar, who began the season at Double-A Akron. Francona expects Salazar to have the normal pre-game jitters all pitchers experience before their first start. "If he has any brains at all, he probably won't sleep a wink and he'll tell everybody tomorrow he did," Francona said. ... The Blue Jays are considering moving Brett Lawrie (sprained left ankle) from third base to second base when he comes off the 15-day disabled list. Lawrie played second Tuesday in a rehab appearance at Triple-A Buffalo. "We're gonna let him do it down there a little bit and we'll kind of look at it when he comes back," manager John Gibbons said. ... RHP Zach McAllister (sprained middle finger) will make a rehab start at Akron on Saturday. Francona said McAllister won't throw his curveball, which caused the injury, on Friday but will use it on his second rehab start. ... RHP R.A. Dickey will start for the Blue Jays in the series finale that will begin at 12:05 p.m.