It was just the third win for the Angels in their last 16 games against Tampa Bay.
Vargas (8-5) gave up a single to Desmond Jennings leading off the bottom of the first. The Rays used a hit-by-pitch and a walk to load the bases before Vargas got out of the jam with a popup and fly ball for an out.
The last two outs in the first inning set off a string in which Vargas retired 20 of the next 22 batters, not giving up another hit until the sixth. He ended up with three walks, two hits and seven strikeouts.
Ernesto Frieri came on in the ninth and got the save, his 28th. He also needed to pitch out of trouble.
Tampa Bay starter Jake Odorizzi (0-1) allowed four hits and two walks in five innings.
The Angels' Hank Conger walked with one out in the second, advanced on an out and scored on a single by Luis Jimenez for the only run Odorizzi gave up.
Kole Calhoun singled with one out in the sixth to drive in J.B. Shuck, who had singled and reached scoring position on a walk to Mike Trout.