Willingham then pulled a 3-2 pitch into the left field stands to put Oakland ahead and the A's held on to complete a sweep of their three-game series with the Orioles.
Guillermo Moscoso (2-0) earned the victory despite allowing four runs on five hits over five innings, walking two and fanning one.
Four A's relievers combined to shut out the O's the rest of the way with Brian Fuentes notching his 11th save in the ninth.
Felix Pie's RBI single triggered a four-run fifth inning for Baltimore.
Britton yielded six runs on 10 hits over 5 2/3 innings in the O's loss.