Kazmir gave up three hits and two walks in his first spring appearance, on March 12, but allowed only a two-out single to Clint Barmes in the second on Tuesday. He struck out two in the first, two in the second and one each in the third and fourth before he left after four shutout innings.
"I was able to mix all my pitches in, and everything felt great," Kazmir said. "My fastball wasn't as accurate as I wanted. It seemed like I was behind and had to come back with secondary pitches. But all in all, everything went well. I'll take that line all day long."
Kazmir likely ends up the A's No. 2 after Sonny Gray was named the Opening Day starter.
"At this point in time, to have that kind of command, I was a little surprised," A's manager Bob Melvin said.
Padres right-hander Odrisamer Despaigne gave up two runs on six hits in four innings, and Matt Wisler was roughed up for eight runs -- seven earned -- in the sixth.
San Diego got on the board in the top of the seventh, when Tommy Medica hit his second homer of the spring, a two-run shot.
Up next: The Padres play the National League West-rival Rockies at Talking Stick at Salt River Fields on Wednesday. Tyson Ross stays in rotation and makes the start. The team has its only March off-day on Thursday, save for Andrew Cashner. It's his day to start, and he is slated to throw 60 pitches in a Minor League game, manager Bud Black said.
Chris Gabel is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.