Although Gausman did his part, the Orioles managed only three hits and lost 2-0 Thursday night to drop their first series since the beginning of June.
Recalled from Triple-A Norfolk to make his second start of the season, Gausman allowed four hits, walked two and struck out seven in 6 1-3 innings. The right-hander struck out seven, tying a career high.
"He gave us a chance to win," manager Buck Showalter said. "We just obviously didn't put much together offensively."
Texas starter Yovani Gallardo gave up two hits and three walks over six innings to extend his run of shutout innings to 29 1-3 — the longest streak in the majors this year and fourth-longest in franchise history.
"Today, honestly, was a little bit of a battle," Gallardo said. "I was falling behind on the count with a bunch of guys."
Keone Kela (5-5) got two outs and Shawn Tolleson worked a perfect ninth to earn his 12th save.
After hitting 10 home runs in the first three games of the series, the Rangers failed to go deep against Gausman and four relievers.
It didn't matter, because Texas used small-ball to grab the lead in the ninth.
After Shin-Soo Choo led off the ninth with a walk from Chaz Roe (2-1) and moved up on a bunt, Martin ended a 4-for-34 slump with a single to center.
"It was an exciting moment for me and for my team," said Martin, who came in batting .224. "To find a way to win a ballgame today was exciting."
Martin came home on a single by Rougned Odor.
"The ball didn't fly like it had been," Texas manager Jeff Banister said. "Gausman had the game in control there for a while and really didn't give our guys a whole lot to hit. We struggled a little bit against him, but we were able to push a couple runs across and felt good about getting away with a W."
Baltimore dropped three of four its first series loss since June 1-4 at Houston.
"It was just a good game overall," Orioles center fielder Adam Jones said. "Both starting pitchers went out and dealt. Their bullpen held us in check, and we cracked first."
Gallardo has not allowed a home run in 51 1-3 innings, dating back to May 24. In nine starts following a Texas loss, the right-hander is 6-0 with a 0.79 ERA.
The Orioles missed two early chances to take the lead. In the first inning, Chris Davis lined into a double play with runners at the corners. In the third, Davis struck out with the bases loaded.
Texas got only one runner past first base until Odor led off the sixth with a liner to center over the head of Jones. Vying for a triple, Odor was thrown out on a relay from Jones to shortstop J.J. Hardy to Manny Machado.
Rangers: Activated RHP Neftali Felize from the 15-day disabled list and optioned starter Nick Martinez to Triple-A Round Rock.
Orioles: Optioned RHP Tyler Wilson to Triple-A Norfolk and recalled Gausman.
Rangers: LHP Matt Harrison (spine surgery) will be activated from the 60-day DL on Friday, according to general manager Jon Daniels. Harrison is expected to make his season debut Tuesday against Arizona, Banister said.
Orioles: 2B Jonathan Schoop (sprained right knee) was scheduled to continue his rehab assignment with Class A Frederick.
Rangers: Josh Hamilton faces his former team when Texas resumes division play at home against the Los Angeles Angels on Friday night. Hamilton played two seasons with LA before being traded back to the Rangers on April 27. "It'll be good to see some of the guys," Hamilton said, "and that's it."
Orioles: Ubaldo Jimenez (7-3, 3.09) seeks to win his career-high fifth start in a row in the opener of a three-game series against the host Chicago White Sox, who will start John Danks (3-8).