Paxton allowed an unearned run in the first on an error, a walk and a passed ball, then was nicked for another run in the second while giving up a pair of doubles.
El Paso scored again in the third on a walk, a double and an RBI single by former Mariners catcher Adam Moore, before Paxton dug in and retired the next three batters to strand runners at first and third.
The 25-year-old is 5-0 with 1.75 ERA in his first six Major League starts, the lowest ERA through that span in club history. He was 2-0 with a 2.25 ERA this year before being shut down in the sixth inning of his second outing.
Meanwhile, right-hander Taijuan Walker is expected to start Wednesday for Tacoma against Salt Lake City in a 7:05 p.m. PT game at Cheney Stadium in what will be his first start since being shut down in mid-April during a previous rehab stint with the Rainiers.
Walker, 21, threw three innings of a simulated game Friday and said he felt great on Saturday.
"That was one of the biggest things, to see how I bounced back today, and I feel really good," said Walker, the No. 6-ranked prospect in baseball by MLB.com. "I'm excited to get back out there on Wednesday and be on my regular five-day routine again."
Walker has yet to throw in a Major League game after being hampered by a sore shoulder since the start of Spring Training. He said he'll throw about 70-75 pitches on Wednesday if all goes according to plan.
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.