The Orioles have captured five of their last six, the last two wins having come against the Red Sox to begin their four-game series.
Tillman (7-2) gave up all three Boston hits and he survived walking a batter in each of the first four innings. He lasted six innings, after which Darren O'Day, Tommy Hunter and Jim Johnson each worked a perfect inning.
Johnson collected his 24th save.
Both the Baltimore runs were given up by Ryan Dempster (4-7), who surrendered five hits and walked four over 7 2/3 innings.
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