Seager sealed the victory with a three-run homer in the eighth inning. In 153 career games against the Rangers, he has 28 homers and 99 RBI, his most against any team.
Texas loaded the bases with one out in the bottom of the first but managed only one run on a groundout by Rougned Odor.
The Mariners stretched their lead to 6-1 in the third when the first two batters, Murphy and Vogelbach, homered against Luke Farrell. Vogelbach drove in two runs, one with a bases-loaded walk in the first.
In the bottom of the third, Rangers rookie Nick Solak tripled home a run and scored on another grounder by Odor.
Newly recalled Rangers right-hander Ian Gibaut retired the first five batters he faced but wildness led to him walking in a run with two out in the fifth for a 7-3 Mariners lead. The Mariners drew nine walks from seven Texas pitchers, who also hit three batters.
Seager's homer increased the lead to 10-3. Tim Lopes drove in the final run with a ninth-inning double.
Kikuchi allowed three runs in five innings. He has exceeded five innings in only one of his last six starts.
The teams split the four-game set. Seattle won the season series 12-7.
There was a moment of silence before the game for the victims of a mass shooting in West Texas on Saturday. Seven people were killed and 22 were injured.
Mariners: SS J.P. Crawford sat out his second straight game because of a tight right hamstring. "He's going to fly back to Seattle," manager Scott Servais said. "Doctors are going to take a look at him. My guess is he's going to be out at least a week."
Rangers: RHP Edinson Volquez(strained elbow) was activated from the 60-day injured list and pitched for the first time since April 4 with a hitless seventh inning. The 15-year veteran is expected to retire at the end of the season. "He's put a lot of effort into the culture of the clubhouse," manager Chris Woodward said. "It's the least we can do for his sake." . Woodward said he didn't know when OF Joey Gallo, recovering from a broken right hamate bone, might return. "I think he's going to take batting practice in New York. It's a little bit sore."
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