Vargas (2-1) struck out seven and walked three over seven innings. Tom Wilhelmsen worked the eighth and Brandon League needed just five pitches to turn in a perfect ninth for his fifth save in as many tries.
Chone Figgins and Ichiro Suzuki both hit solo homers in the first off Derek Lowe (1-2). Jesus Montero drew a bases-loaded walk in the second to drive in another Seattle run and Dustin Ackley had an RBI single in the fourth.
The only Cleveland run came on a sacrifice fly by Jason Kipnis in the third. The Indians had a four-game winning streak snapped.
Wisconsin business offering 'therapeutic cuddling' forced to close
Megyn Kelly: Santa Claus and Jesus are both white men