Tepesch, back from the minor leagues, earned his first major league victory in more than 10 months and the Rangers edged the Seattle Mariners 4-3 on Wednesday.
Ross, back in the bullpen after an unsuccessful stint in the rotation, bailed Tepesch out of a seventh-inning jam.
Neal Cotts, whose ERA has ballooned from 1.11 in 2013 to 4.34 this season, had a strong eighth.
Joakim Soria, back in a closer's role this year for the first time since 2011, pitched a perfect ninth inning for his eighth save in eight opportunities.
The Rangers' offense had three first-inning runs and Shin-Soo Choo's leadoff home run in the bottom of the fifth that broke a 3-3 tie.
Choo's fifth homer went into the bullpen in left-center.
"Two strikes, I was in a rough spot. I think about more (getting) on base," he said.
"Got a home run that got up in that gust a little bit, that's it," Mariners manager Lloyd McClendon said. "It's a tough ballpark to pitch in, but I thought (Chris Young) did a pretty darn good job for us.
Texas turned two double plays. The second was on Ross' second pitch after entering the game with one out and runners on first and second for the Mariners. Pinch hitter Stefen Romero grounded to Adrian Beltre, who stepped on third base and threw to first to complete the inning-ending double play.
"I was thinking, 'Gosh, here we go! I'm in a situation where I like to be.' I was pretty amped," Ross said. "I wanted to be out of that inning without those runs scoring."
Tepesch (1-0) allowed five hits and two walks in 6 1-3 innings for his first win since defeating Houston 10-5 on July 5, 2013. The second-year pitcher threw a career-high 112 pitches.
It was his second start this season for the Rangers after being recalled from Triple-A Round Rock, where he was 6-1.
Texas manager Ron Washington has noticed a difference.
"He has an out pitch right now. He's got that slider working, and he's able to locate his sinker. With that going on and commanding the baseball, I think there's the difference right there."
Washington visited Tepesch on the mound with one out in the seventh and Dustin Ackley coming up.
Tepesch assured the manager he was OK. Then he walked both Ackley and John Buck.
"I just wanted to know how he was feeling," Washington said. "Did he think he had enough to get this lefty up there? Because I had a lefty ready. The look in his eyes, he convinced me, and I had to end up getting Robbie to bail me out."
After that, it was Cotts striking out Robinson Cano, who had homered earlier, and Seager, who entered the game with a .358 average in Arlington, with a runner on second base in the eighth.
Against former Rangers right-hander Chris Young (3-2), Daniel Robertson led off the first with a walk and scored on Elvis Andrus' homer. Alex Rios singled home the third run.
Seattle tied it in the fourth. James Jones tripled and scored on Michael Saunders' single.
Cano then hit his two-run homer. Center fielder Michael Choice ran back to attempt a catch, but his glove hit the wall as the ball barely cleared it.
Seattle had only one baserunner against Tepesch in the first three innings: Seager on a leadoff single in the second. He was erased in an unusual 4-5-3 double play. With Texas' defense shifted to the right, Smoak grounded to second baseman Luis Sardinas, who threw to Beltre covering second. Beltre's relay throw to first beat Smoak.
Young gave up seven hits and three walks in 6 1-3 innings.
"You have those games where if you can limit the damage early, you feel like you'll pitch a good game, and I gave up one too many in the first," Young said.
NOTES: Rangers first baseman Prince Fielder (neck) missed a fourth consecutive game, and center fielder Leonys Martin (stiff neck) was not in the starting lineup for the second game in a row. Martin entered the game as a defensive replacement in the ninth. ... The teams split the two-game series.