Tillman controlled the Rangers who managed six hits and three walks but only two runs off the right-hander, who struck out seven. Tillman extended his dominance against American League West opponents, improving to 11-1 in 13 career starts.
Tillman was lifted in the ninth after yielding a leadoff homer to Adrian Beltre that cut the Orioles lead to two runs. Brian Matusz entered and fanned A.J. Pierzynski for the inning's first out, then issued a base-on-balls to pinch-hitter Jurickson Profar.
Darren O'Day was called on to record the final two outs for his second save, handing Baltimore a three-game road sweep and a fourth straight victory overall.
Baltimore entered game in third place in the AL East, 3 1/2 games behind Boston.
Martin Perez (3-3) was the losing pitcher, giving up four runs on nine hits over 6 1/3 innings.
Ian Kinsler went 2-for-4 with an RBI as Texas fell three games behind AL West-leading Oakland with a fourth consecutive defeat.
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