"It's a broken record talking about him because we're seeing basically the same game out of him," Melvin said. "I had heard last year maybe this is a 100-pitch guy tops, six innings maybe. He's been anything but. He's been absolutely terrific."
Kazmir (9-2) went into the game with the second-lowest ERA among qualifiers in the American League and extended his streak to 18 1/3 innings without allowing an earned run before Dustin Pedroia hit a two-run home run in the sixth. He struck out eight and didn't walk a batter.
Over his past five starts, Oakland's right-hander is 4-0 with a 1.27 ERA.
"Probably one of the best (games) I felt this year, for sure," said Kazmir, who has allowed two runs or fewer in each of his past five starts.
"I was able to get ahead most of the time with my fastball and expand the strike zone with my breaking balls and my changeup. Didn't really use too many breaking balls. Just relied mainly on fastball location."
Stephen Vogt had two hits and two RBIs, Jed Lowrie scored twice, and John Jaso singled in an insurance run in the seventh to move the A's a season-high 17 games over .500. It's the best record in the majors and continued Oakland's best start since 1990.
Cespedes had not homered against the Red Sox until his two-out, solo shot off Jake Peavy in the third.
Boston had played five straight one-run games heading into the series opener with Oakland. This one was tight as well.
The A's led 3-0 after Vogt's single scored Lowrie in the fourth.
Kazmir, who hasn't lost since May 23, took a shutout into the sixth that Pedroia ended with a two-out home run.
It was the only mistake Kazmir made.
"We faced a tough pitcher," Pedroia said. "To be honest, our at-bats weren't that bad. We have to find a way to have a big inning and get some momentum."
Peavy (1-5) had a second straight strong outing but remained winless over his past 10 starts. Peavy allowed five hits over 6 1/3 innings, retired eight of the final nine batters he faced and struck out four with three walks.
It wasn't enough to prevent the Red Sox from ending their three-game winning streak.
Vogt hit an RBI groundout off Peavy in the second and singled in another run in the fourth. Lowrie, who walked and doubled, scored both times.
Cespedes homered with two outs in the third. The Cuban slugger is batting .343 with four home runs and 12 RBIs through 17 games in June.
Cespedes has driven in 49 runs already this season and could soon join teammates Brandon Moss (55) and Josh Donaldson (52) in the 50-RBI club.
"When you look at the runs that we've put up this year, a lot of it has to do with those guys in the middle of the order," Melvin said. "It's pretty amazing."
Otero was in the closer's role because Sean Doolittle had pitched in the previous two games. ... Cespedes has now homered against every team in the AL except Tampa Bay. ... RHP Clay Buchholz (hyperextended knee) pitched six scoreless innings during his second rehab start for Triple-A Pawtucket. ... LHP Brad Mills starts Friday in his Oakland debut. Mills was acquired in a trade from Milwaukee earlier this week. LHP Felix Doubront (2-4) pitches for Boston.
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OAKLAND, CA - JUNE 19: Jake Peavy #44 of the Boston Red Sox pitches against the Oakland Athletics during the...