Tampa Bay's winning rally started when Sean Rodriguez singled with one out off Orioles reliever Mike Gonzalez (0-1) and moved to third on Kelly Shoppach's double. Jason Bartlett was intentionally walked to load the bases and Crawford stroked the game-winner.
Rafael Soriano (1-0) was credited with the win after pitching a scoreless ninth.
The Orioles got homers from Adam Jones, Luke Scott and Matt Wieters in the defeat.
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