Davis had a bases-loaded double after Adam Jones drove in two runs with a single in Baltimore's five-run fifth inning. Davis added his 16th home run this year in the seventh.
Orioles starter Chris Tillman (3-1) gave up two runs and five hits in six innings of work. He walked four and struck out five. Two of the hits came in the seventh when the Rays' Sam Fuld drove in two runs with a double.
But by then Baltimore had knocked Tampa Bay starter James Shields (8-7) for five runs and three hits in the fifth inning. Shields helped the rally with a hit batter and two walks. He gave up a total of six hits and walked five, while striking out five, in six innings.
Nick Markakis started the fifth-inning rally with a single. J.J. Hardy was hit by a pitch and Jim Thome walked, loading the bases ahead of Jones's two-run single. After Matt Wieters walked, Davis plugged the gap in left-center to clear the bases.