Dustin Ackley, struggling with just four hits all season, provided the winning hit, an RBI single in a two-run sixth.
"It started off with a nice cold bucket of ice water and some milk and some ketchup. It was good," Maurer said of the postgame celebration.
Maurer (1-2), rocked for seven hits and six runs in just two-thirds of an inning in his previous outing Tuesday against the Astros, allowed three runs (two earned) on five hits in six innings against the hard-hitting Rangers. He struck out five and walked one.
"It's nice to see him get his first win," manager Eric Wedge said. "He was more in control today, more at ease, more comfortable. He was noticeably different with his poise and the way he handled himself."
He was different because he was himself. He said he was "free," pitching the way he did this spring, the way he won a spot in the rotation.
"Just being free with my arm and not being tight up top," Maurer said. "It was fun knowing my stuff will play.
"It was a game where I'm not looking at hot zones or cold zones for the hitters. I pitched my game. Back to basics."
Rangers shortstop Elvis Andrus said Maurer "kept the ball down and threw a lot of strikes. He had a pretty good slider. He just didn't let us get comfortable."
Rangers manager Ron Washington added: "We're facing a good pitching staff today. They pitched, we pitched. They just happened to get the run that put them over the top."
Trailing 3-2 in the sixth, Kyle Seager started the winning rally with a one-out double into the right-field corner. Jesus Montero blooped a single to right, scoring Seager with Montero taking second on the throw. Ackley then lined a single up the middle to score Montero.
"That was really huge for us. I think you can see we're capable of getting hits in bigger situations," said Ackley, who was 4-for-37 before his clutch single. "That's all we've been away from winning some ballgames, one or two hits. Today, we showed we can do that."
Raul Ibanez hit his second home run, a solo shot in the fourth while Seager roped a pair of doubles.
The Rangers scored first, a two-out run in the second. Geovany Soto singled to center and Mitch Moreland followed with a run-scoring double into the right-center field gap.
The Mariners responded in the bottom of the inning with a run on back-to-back doubles by Justin Smoak and Seager.
Ibanez's home run came on a 1-0 pitch from Nick Tepesch, giving the Mariners a 2-1 lead. It was his 68th home run at Safeco, the most by any player.
The Rangers came right back in the fifth with a couple runs to take a 3-2 lead. Maurer worked out of one jam, but not a second one.
After Leury Garcia's one-out triple that caromed off the top of the right-field wall, Wedge brought the infield in. That worked nicely, as Andrus bounced to Ackley at second base, who threw home to nail Garcia.
However, the Rangers continued to reload with two outs. Andrus stole second. Craig Gentry was hit by a pitch. Lance Berkman followed with a single through the right side, sending Andrus home and Gentry to third. Gentry then raced home on a passed ball by Montero.
Tom Wilhelmsen picked up his fifth save, allowing his teammates to haul Maurer into the shower.
"It's awesome having the whole team around you," Ackley said. "You're just getting soaked. It's cold, but it's an awesome, awesome feeling."