Odrisamer Despaigne, competing for a spot in the Padres' starting rotation, allowed two runs on six hits over four innings. He struck out two and did not walk a batter.
Kazmir was sharp, allowing only a hit to Clint Barmes and striking out six, including four of the first five batters he faced.
"I'm not looking at the results as much as I'm looking for how batters react to my pitches," Kazmir said. "At the same time, I'll take that line all day long. I had good life on my fastball but I was not as accurate as I wanted."
Zobrist hit his first home run of the spring in the fifth to give the A's a 5-0 advantage. He became the first A's player to record at least one double, one triple and a home run. Matt Olson drove in the first two runs.
A's outfielder Coco Crisp was in the lineup for the first time in a week after letting his elbow quiet down. He was in left field and is getting instruction from Rickey Henderson.
A's manager Bob Melvin said he likes that Crisp did not hesitate stealing second after working a walk with one out in the fifth.
"He's a guy with speed, who can hit to either side and has power," Kazmir said. "He gives the opposing pitcher more to worry about."
Fuld batted second behind Crisp and played center. "He can beat you in so many ways," Fuld said. "I love hitting behind him."
Padres: Despaigne, who was 4-7 with a 3.36 ERA in 16 starts last year, is making a solid case to open the season in the rotation. He allowed his first earned runs of the spring in the fourth inning and now has an ERA of 2.08 in three appearances, two starts. He's walked two and struck out six. "I am ready if they need me to start or to pitch in the bullpen," Despaigne said through an interpreter following his last start. "I'm used to starting and I want to be No. 1 or No. 2 sometime."
A's: Kazmir likes the progression of throwing in simulated games before appearing in games. "I feel stronger," he said. "I feel like I came into camp with better velocity as far as just getting into it. Last time out it was tough to hone my energy in when it's the first time. It was more about adrenaline then."
Kazmir was so efficient; he needed to throw 10 extra pitches in the bullpen after he was pulled. "They were all fastballs and it was to stretch me out a little more," he said.
A's LHP Sean Doolittle (shoulder) will move up to throwing rag balls next week after throwing weighted balls.
The Padres played their only split-squad games of the season and played their lone spring game against Oakland. ... The A's have won nine of the last 13 exhibition games played with the Padres. ... Both teams will take their only day off during the spring on Thursday.
Padres: Tyson Ross will make the start on Wednesday when they travel to the Colorado Rockies.
A's: Drew Pomeranz pitches against the Seattle Mariners in Peoria on Wednesday.