Tepesch came out of the game in the second inning after he was hit just above the right wrist by a line drive, sustaining a bruise.
Lowe (1-0) allowed only one Seattle batter to reach when he hit Kendrys Morales with a pitch leading off the third.
"This is what I signed up for," Lowe said. "You never know when that day is going to come. I pride myself on being prepared."
This was Lowe's longest outing since going four innings with the New York Yankees against the Rangers last Aug. 13.
After not pitching for 10 days, Lowe went 2 2/3 innings Thursday against the Chicago Cubs.
Lowe turned to his sinker against the aggressive Mariners lineup. He needed only 31 pitches to record 12 outs.
"To throw 31 pitches in four innings, that's not just the pitchers," Lowe said. "It takes two to tango, so to speak. I tried to throw as many sinkers down in the zone as I possibly could."
Tepesch left with two outs in the second inning when Jesus Montero's liner caromed off the right-hander's wrist and into shallow right field.
The 24-year-old Tepesch, who was bleeding just above his wrist, began immediately shaking his arm after he was struck. He threw a couple of warm-up pitches, but the Rangers opted to bring Lowe into the game.
In his third career start, Tepesch allowed two hits in 1 2/3 innings. Texas manager Ron Washington said he expects the rookie to make his next start.
"It could have been a lot worse," Tepesch said. "I'm just fortunate the results weren't too bad."
Seattle starter Brandon Maurer (1-3) gave up the homers to Pierzynski and Murphy, the only two hits the rookie allowed in 6 2/3 innings. The 22-year-old struck out two and walked three.
The Mariners had five singles and were shut out for a second straight game. Seattle has gone 19 innings without scoring a run.
"We hit some balls hard tonight," Seattle manager Eric Wedge said. "We're in one of those zones right now where if you do hit it hard, it's right at them. We're going through some tough times offensively right now."
Joe Ortiz relieved Lowe with two outs in the sixth and allowed two batters to reach when Kyle Seager singled and Morales walked. Ortiz got out of trouble when Michael Morse grounded out to end the sixth.
The Rangers broke the game open with three runs in the eighth. Lance Berkman had a two-run single and Pierzynski capped the inning with an RBI single.
"The last two nights have been a step in the right direction," Murphy said. "But I think it's safe to say our offense still has yet to completely click. While we're still trying to find ourselves one through nine, our pitchers are going to keep us in games and our pitchers are going to win games for us."
Texas picked up its first hit when Pierzynski homered to center off Maurer with one out in the fourth.
Seattle center fielder Franklin Gutierrez reached out over the wall and nearly bumped gloves with the fan who caught Pierzynski's home run ball.
Wedge said that Gutierrez told him he thought he was going to make the catch, but he admitted that the play was not fan's interference.
Maurer retired the next 10 batters he faced until Murphy homered with two outs in the seventh. That chased the rookie and Charlie Furbush came on in relief.
The Mariners had two runners on in each the seventh and eighth innings but couldn't score. Seattle has scored 19 runs in its last 10 games.
The Mariners have struck out 52 times in its last four games.
"It's been two well-pitched ball games on their side," Seager said. "Offensively, we've obviously got to do better and score some runs."
Justin Grimm, who is replacing the injured Matt Harrison in the rotation, will make his second start of the season for the Rangers on Sunday. He will oppose Mariners right-hander Aaron Harang (0-1). ... Seager extended his hitting streak to nine games. ... Texas SS Elvis Andrus is 5 for 35 in his last nine games.