The veteran right-hander had a no-hitter through 8 2/3 innings before Shannon Stewart hit a single to right field to break up Schilling's bid for his first career no-hitter.
David Ortiz drove in the game's lone run with a solo homer in the top of the first.
Schilling (6-2), who was pounded by the New York Yankees in his previous start Saturday, did not walk a batter and struck out four.
Oakland's Joe Blanton (5-4) surrendered an earned run and four hits in 7 1/3 innings with three walks and two strikeouts.
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