Baker, who had been sidelined for 11 months while rehabbing from Tommy John surgery, made only 23 pitches before departing, though he was scheduled for two innings. He's not expected to be ready to pitch in the regular season until mid-April.
It was right-hander Cory Wade who surrendered the A's second homer of the day, this one coming off the bat of Donaldson with two runners on base in the third. Then, in the seventh, Rosales launched a two-run go-ahead shot off reliever Jason Berken. Rosales doubled his output with another two-run homer in the eighth.
The A's also got four hits from Eric Sogard, who is now 15-for-30 and keeping his name in the second-base competition.
Chicago, meanwhile, scattered four runs on eight hits off lefty starter Tommy Milone, who walked none and fanned two in his 4 2/3-inning outing.
Outfielder Dave Sappelt homered off the southpaw in the second and again caused damage in the fourth, notching a two-run single.
In the fifth, shortstop Javier Baez collected an RBI double off lefty Hideki Okajima, and the Cubs put two more on the board in the sixth, again getting to the reliever by way of a two-run homer from Brent Lillibridge.
Up next: Right-hander A.J. Griffin is scheduled to take the mound at home on Monday, when the Mariners pay a visit for a 1:05 p.m. PT start. Right-hander Hisashi Iwakuma will start for Seattle.
Closer Grant Balfour is also scheduled to pitch in a game for the first time this spring on Monday, following a month-long rehab from knee surgery. It's not yet known whether he will pitch against the Mariners or in a Minor League game, though manager Bob Melvin said on Sunday morning the latter is more likely.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.