The Sox offense, which scored all of their four runs off Orioles' starter Rodrigo Lopez, tied the game up in the second with back-to-back doubles by Paul Konerko (run) and Carlos Lee (RBI), and back-to-back sacrifice flies by Armando Rios and Joe Crede, scoring Lee.
The Sox managed just three more hits the rest of the game, and failed to score on a key bases loaded situation in the fifth with Konerko grounding out to end the inning.
Stewart allowed just two hits -- both singles -- after the first, before leaving after five innings and 93 pitches for Kelly Wunsch. Wunsch threw a scoreless sixth inning, but Rick White struggled in the seventh, giving up a homer to Deivi Cruz and a double to Mora.
Tom Gordon relieved White, and after striking out Jose Leon, he gave up the eventual game-winning two-run home run to Matthews. Damaso Marte threw a scoreless eighth inning and the Sox were retired 1-2-3 in the ninth by Jorge Julio, who recorded his sixth save.
At 12-10, the Sox will now face the Minnesota Twins starting Friday at U.S. Cellular Field. Mark Buehrle, Jon Garland and Esteban Loaiza are scheduled to pitch in the series, with the Twins countering with Joe Mays, Kyle Lohse and Rick Reed. Friday's game will start at 7:05 p.m. CT and will be televised on Fox Sports Net Chicago.