Tillman (1-0) gave up five hits, including Torii Hunter's solo homer in the fourth, in 8 1-3 innings. Tommy Hunter entered with one out in the ninth and Victor Martinez on second base and retired the last two batters for his second save.
Baltimore won for the first time since its opener against baseball's last undefeated team.
Verlander (0-1) gave up two runs on five hits and two walks over eight innings.
Adam Jones drove in the go-ahead run in the eighth with a sacrifice fly after Nick Markakis tripled.
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