Kazmir, a left-hander who signed a two-year, $22 million deal with the A's over the winter, gave up two hits and struck out two.
Left-hander Wade Miley had a strong effort for Arizona, pitching five innings and giving up an unearned run on three hits. He walked one and struck out four.
Daric Barton drove in Oakland's second run with a single in the eighth.
Diamondbacks: Manager Kirk Gibson was impressed with Miley's second start of the spring.
''He had good arm motion, was throwing most of his pitches in all counts. He was keeping the ball down,'' Gibson said. ''He threw his slider, curve, change and fastball, and he is getting more consistency on his slider.''
Athletics: After pitching in a game with Oakland for the first time, Kazmir said: ''Now it feels like I'm actually contributing. I tried to keep my emotions in check and not do too much.''
''In that third inning I started getting tired, but all in all I am pleased,'' he said.
Diamondbacks: Veteran right-hander Bronson Arroyo, who signed with the team as a free agent, is moving slowly but surely toward a return to game action. Scratched from his start Tuesday with a bulging disk in his lower back, Arroyo will play catch on Saturday.
''We are encouraged right now,'' Gibson said.
First baseman Paul Goldschmidt is expected to return to the lineup in one of the team's split-squad games Saturday after missing two games with leg stiffness, Gibson said.
ON HIS WAY
Left-hander Oliver Perez and the Diamondbacks have agreed to a $4.25 million, two-year contract, according to a person familiar with the negotiations. The person spoke on condition of anonymity Friday because the agreement was subject to a successful physical.
The 32-year-old Perez was 3-3 with a 3.74 ERA last year in his second season with the Seattle Mariners after spending 2011 in the minors. He has a 62-75 record in 195 starts and 105 relief appearances over 11 big league seasons.
BURNS CUT DOWN
Oakland outfielder Billy Burns, who leads the majors with seven stolen bases this spring, fell short in his bid for No. 8 when he was thrown out at second by Diamondbacks catcher Henry Blanco in the third inning.
EYE ON PRADO
Veteran infielder-outfielder Martin Prado was moved all over the field like a chess piece last season, but that might not be the case this year, Gibson said. Prado likely will receive the lion's share of his playing time at third base.
''I think I understand him better,'' Gibson said. ''If it is right, I will move him, if one of the other guys is nicked up.''
AP Sports Writer Ronald Blum in New York contributed to this report.