Tillman (4-2) scattered five hits and a walk while striking out three. His dominant outing came one night after Wei-Yin Chen and four relievers combined to beat Kansas City 2-1.
Jeremy Guthrie (2-3) bounced back from a lousy start to last eight innings against his former team. The Royals' starter allowed four runs, eight hits and a walk while striking out two.
While falling to 0-3 with four no-decisions in his last seven starts, Guthrie at least was able to save a bullpen that had been chewed up in that close loss the previous night.
Meanwhile, Tillman lasted more than six innings for the first time since April 11, a span of five starts. The Orioles' right-hander won for the first time in four starts this month.
The game was played in a brisk 2 hours, 22 minutes, mostly because the starters were so effective. Tillman retired 13 of 14 batters after giving up a double to Norichika Aoki to start the game, and Guthrie only allowed a single by J.J. Hardy over the first three innings.
Baltimore finally got to Guthrie in the fourth, and it was partly his own doing.
Manny Machado led off by bunting back toward Guthrie, and he slipped while trying to field the ball. His hurried throw to first was wide of the bag for an error, and Machado trotted over to second base. Moments later, he headed for third when Guthrie threw a wild pitch.
Davis walked to put runners on the corners for Cruz, whose single drove in the game's first run. Clevenger then grounded into a fielder's choice to give the Orioles a 2-0 lead.
It remained that way until the sixth, when consecutive singles again put runners on the corners. Cruz then lofted a fly ball deep enough to center to bring home Adam Jones.
Davis added his third homer of the season with two outs in the eighth.
By that point, the only drama was whether Tillman would finish the game. The Orioles had two relievers up in the bullpen in the ninth, and the Royals got the leadoff man on base. But Tillman calmly got the next three batters to ground out to end the game.
NOTES: The Orioles recalled RHP Brad Brach from Triple-A Norfolk and designated RHP Evan Meek for assignment. ... The Royals selected the contract of RHP Casey Coleman from Triple-A Omaha and designated OF Justin Maxwell for assignment. Coleman retired the side in the ninth. ... Baltimore RHP Bud Norris is scheduled to start Saturday. LHP Danny Duffy will start for Kansas City.