Vargas (9-7) threw 110 pitches, retiring 15 consecutive batters at one point and striking out five en route to his fifth shutout and 10th complete game in 153 career starts.
The A's, who clinched their second straight division title Sunday, remain a game behind the Red Sox for the best record in the majors following Boston's 8-3 loss at Colorado.
"I think anytime you go up against a team that won the division, you want to pitch well and give it your best," Vargas said. "It was definitely a better game than the last one. I was able to control counts and was able to throw fastballs and curveballs. That made the changeup more effective."
The left-hander, who was acquired from Seattle for slugger Kendrys Morales, is 3-3 with a 4.64 ERA in his past nine outings after missing almost two months because of a blood clot near his armpit.
"That tells you a lot about how hard he worked to come back and the professional that he is," pitching coach Mike Butcher said. "He's pitched great baseball for us. We definitely missed him in the rotation those two months he was gone, because he's going to give you a chance to win every time he takes the ball. He definitely knows how to go out there and compete, and he's picked us up these last nine starts."
Vargas becomes a free agent after the season and is hoping to be back with the Angels.
"I didn't put any more importance on this one than any other start, regardless of the fact that I was (on the disabled list) or not," he said. "I was throwing good before that. And when you come back from something like that, you've got to make do with what you've got and let the chips fall. I definitely want to go out and pitch well every time out, but that's not going to happen."
A.J. Griffin (14-10) gave up three runs and five hits over five innings. The 25-year-old right-hander was 4-0 in his previous five outings, including a no-decision Wednesday against the Angels when he retired 17 of his final 18 batters and allowed one hit over six innings -- a two-run homer by Mike Trout.
"A.J.'s been consistent all year," manager Bob Melvin said. "Like anybody, he's had a rough stretch or two. But if you look at the overall body of work, it's been a pretty consistent year for him and something to be proud of. Based on the way he pitched last year, this is about what we expected -- to be consistent and keep his team in games and win his share of them. And he's done all that."
Griffin finished his first full big league campaign with a 3.83 ERA, 171 strikeouts in 200 innings and a major league-worst 36 home runs allowed. The Oakland single-season record in that department is held by Catfish Hunter, who gave up 39 in 1973 and still won 21 games.
"I feel pretty good about the season I've had," Griffin said. "It's just about being competitive, pounding the strike zone and getting ahead of guys. Home runs happen, but it's just part of baseball. I'm just trying to contribute here. We've got a great thing going on with this club, and I look forward to being a part of it and doing great things here."
For the second straight night, Kendrick homered his first time up after not hitting one in his previous 30 games. The Angels increased the margin to 3-0 in the third on Josh Hamilton's two-out, two-run single with the bases loaded.
The advance sale for Wednesday's home finale will easily put the Angels over the 3 million mark in attendance for the 11th straight season. They are 16,721 shy. ... First-base umpire John Hirshbeck called Yoenis Cespedes safe and then out on a bang-bang play in the seventh as second baseman Kendrick fielded the ground ball up the middle and completed an inning-ending double play. ... Vargas' other shutout this season was a three-hitter against Baltimore on May 3 in Anaheim. ... Kendrick homered in back-to-back games for the second time this season. He also did so July 5 and 6 against Boston. ... Trout, who was presented with the Gene Autry Trophy before the game as the team's MVP for the second straight year, hasn't homered in his past 15 home games and 52 at-bats at Angel Stadium since going deep in back-to-back games Aug. 6 and 7 against Texas. ... Josh Donaldson made his 153rd start at third base, the most by an A's player at that position since Sal Bando in 1976 (155).