Matt Wieters had two hits and scored twice to help the Orioles (56-43) move a season-high 13 games over .500 with their seventh victory in eight games. They sure seem comfortable in Texas, where Baltimore won last year's AL wild-card game.
Consistent starting pitching has been the key to this run. Tillman (12-3) gave up two runs and six hits while striking out seven, making Baltimore starters 7-1 in the last eight games.
The 25-year-old righty was added to the AL All-Star team as an injury replacement but did not pitch Tuesday night at Citi Field.
He looked plenty fresh over eight-plus innings in Arlington, holding the slumping Rangers in check until Adrian Beltre chased him with a leadoff homer in the ninth. That sent Tillman to the dugout three outs shy of his first career complete game.
Darren O'Day got two outs against his former team to earn his second save.
Texas has dropped four straight and seven of eight.
Martin Perez (3-3) pitched 6 1-3 innings for the Rangers, giving up four runs and nine hits. He didn't get much help from his defense.
Neal Cotts, Joakim Soria and Cory Burns came out of the bullpen to combine for 2 2-3 shutout innings. Texas relievers have thrown 19 2-3 consecutive scoreless innings.
It was the bottom half of the Baltimore lineup that did the most damage. The last five hitters in the order scored all four runs, drove in three and had seven of the Orioles' 10 hits.
Nate McLouth led off the game with a single for the third straight game, but Baltimore didn't really get going until the second inning. That's when Rangers left fielder David Murphy lost Chris Davis' fly ball in the sun for a leadoff double. Davis scored on Wieters' single for a 1-0 lead.
Rangers shortstop Elvis Andrus made an error on potential double-play grounder that instead left the bases loaded with nobody out. Brian Roberts singled to make it 2-0, but Perez got out of the jam with consecutive strikeouts and a groundout.
In the third, Wieters doubled past a diving Beltre at third base and J.J. Hardy put the Orioles up 3-0 with a double that sailed over Craig Gentry's head in center field.
Baltimore added its fourth run in the fourth. Roberts started the inning with a double and scored on Manny Machado's single that caromed off Perez's glove and into center field.
Texas scored in the fifth on Ian Kinsler's RBI single to right, but Murphy got caught in a rundown between third and home and was tagged out by Wieters. That made it twice in three games that a Rangers runner was thrown out after rounding third and trying to get back to the bag.
Beltre's home run was the first by a Rangers player since his two-run shot in the ninth inning against Detroit on July 13.
NOTES: Rangers LHP Matt Harrison, on the disabled list because of a herniated disk that required two operations in late April and early May, threw a 45-pitch bullpen session Saturday and will throw 60-65 pitches Monday. The team's opening day starter said he plans to throw batting practice Wednesday. "My goal is the end of August or early September, but if things go good, maybe we can speed that up," Harrison said. ... Rangers RHP Alexi Ogando (shoulder inflammation) is slated to come off the disabled list Tuesday and start against the New York Yankees. His last appearance was against Boston on June 5.