Texas starter Colby Lewis went the distance but he received little support in the eighth loss for the Rangers in 11 games.
Vargas (2-2) gave up a run on six hits and was helped out by Jamey Wright in the eighth. Texas scored its only run in the eighth and had the potential tying runs on base when Wright came on to get Adrian Beltre to hit into a force out to end the threat.
Brandon League worked a 1-2-3 ninth for his ninth save.
Smoak put Seattle in front with a solo homer in the second. Luis Rodriguez doubled home a run in the third and Ichiro Suzuki had an RBI single in the seventh.
Lewis (2-4) went the distance for just the second time in his seven major league seasons. He gave up eight hits and struck out 11.