Mikolas faced two batters over the minimum, erasing two of the three hits he allowed with double plays. The right-hander struck out five and walked one. It is the first time Mikolas has not allowed a run in 10 career starts.
Neftali Feliz pitched the ninth for his seventh save in eight attempts.
Seattle starter Roenis Elias struggled with command, walking four, but was able to limit the Rangers to one run in five innings. The rookie stranded runners in scoring position in three innings before giving way to the bullpen after tossing 101 pitches.
Rougned Odor padded the lead with an RBI groundout in the seventh, scoring Leonys Martin from third.
The Rangers' best opportunity to break the game open came in the fourth, but Adam Rosales flew out to end the threat with the bases loaded. Texas left five men in scoring position.
Mariners: 2B Robinson Cano was in the lineup and batting third on Monday, a day after removing himself from the field due to the effects of an illness. Manager Lloyd McClendon said before the game that Cano was feeling better and it didn't appear the bug hit anyone else on the team.
Rangers: Texas placed OF Shin-Soo Choo on the disabled list Monday, ending his season. Choo will have surgery to remove a bone spur in his left elbow in the next couple weeks and the expectation is for him to be healthy enough to have a normal offseason. ... General manager Jon Daniels said the Rangers plan to activate LHP Derek Holland from the disabled list after his start Thursday for Triple-A Round Rock.
Mariners: LHP James Paxton looks to rebound from his first Major League loss in his 11th career start. Paxton has never faced the Rangers.
Rangers: RHP Nick Martinez looks to finish the season strong after getting out to a 3-9 start with a 5.13 ERA. Martinez allowed one run in six innings in his only start against the Mariners, but was outdueled by Hisashi Iwakuma.