Josh Donaldson hit a two-run homer and Stephen Vogt drove in three runs for the A's, who won three of four in the two-city series that began Monday night in Oakland. The A's (58-34) have won seven of eight overall and have matched the best start in Oakland history.
Tim Hudson (7-6) was unable to make it out of the sixth inning and lost his fourth straight decision for the floundering Giants.
San Francisco has lost 15 of its past 19 home games and hasn't won consecutive games here in more than a month.
The game ended on a replay review when A's manager Bob Melvin challenged a call that Vogt pulled his foot off first base on an infield hit by Gregor Blanco. The replay showed Vogt kept his foot on the bag, leading to the final out.
Kazmir (11-3) got the best of a heralded matchup against Hudson, allowing three hits and one walk. Kazmir has allowed one run or fewer in 11 of 19 starts this season for a 2.38 ERA.
Kazmir retired the first eight batters before walking Hudson and didn't allow a hit until Michael Morse's leadoff single to center in the fifth.
Kazmir struck out Brandon Belt and Brandon Hicks before Blanco doubled Morse to third base to snap a 19 at-bat hitless streak. Hudson then hit a drive to deep left-center that Craig Gentry ran down on the warning track for an inning-ending catch.
The A's broke the game open in the top of the sixth when they put together four straight extra-base hits to open the inning against Hudson, including a two-run homer by Donaldson over the right-field wall.
This marked the first time Hudson allowed four straight extra-base hits, according to STATS LLC.
Hudson allowed six runs and nine hits in 5 1/3 innings and lost for the second time in his career against the A's. Hudson spent the first six years of his career in Oakland and has beaten every team in the majors except the A's and Atlanta.
A's All-Star OF Yoenis Cespedes went 0 for 5 with four Ks and hit into a double play. ... Home plate umpire Adrian Johnson left the game before the top of the fourth after being hit in the mask by a foul ball in the first inning. Crew chief Angel Hernandez moved from second base to behind the plate and the game finished with three umpires. ... Tim Lincecum gave a hat and ball from his no-hitter last month to the Hall of Fame. ... Lincecum (8-5) goes for his fourth straight win Friday when the Giants open a three-game series against Arizona. ... Jeff Samardzija (1-0) will make his second start for Oakland when the A's open a three-game series in Seattle against Felix Hernandez (10-2) and the Mariners.