Kazmir's injury isn't believed to be serious, but he did see an orthopedist. Manager Bob Melvin said he will wait to see how Kazmir looks Tuesday before deciding when he'll pitch again.
It was part of a difficult day for Oakland, which lost pitcher Jarrod Parker for the season. The promising right-hander will have elbow ligament replacement surgery next week after an MRI in Florida determined the need for the operation.
''Obviously in this situation, the first thing is you feel bad for Jarrod,'' assistant general manager David Forst said. ''He worked hard this offseason after having some struggles at the end of the year and was hoping to be at the top of the rotation this year.''
Parker had a 10.61 ERA in three spring training starts.
Cubs starting pitcher James McDonald threw two pitches and had to leave with right shoulder soreness. McDonald's second pitch to Coco Crisp sailed over Crisp's head to the backstop, prompting a visit from manager Rick Renteria and a trainer.
''He was shaking his arm so we went out there just to talk to him, and he just felt like his arm wasn't feeling right,'' Renteria said. ''So we're not taking any chances.''
Joe Savery, who had made five relief appearances without a start this spring, took Kazmir's place and shut out the Cubs on two hits in two innings. He struck out five and walked one.
Melvin said Savery is in the mix to make the major league club as a reliever.
Moss scored two runs against the Cubs, and Punto had two RBIs.
CHICAGO: McDonald's spring ERA is 12.71. He has eight walks and no strikeouts in 5 2-3 innings. Renteria wouldn't address the chance that McDonald won't be in the club's starting rotation, saying he wants to make sure McDonald is OK first.
OAKLAND: Savery said he hadn't started a game since 2010 at the Triple-A level. ''I think my slider's probably as good as it's ever been,'' he said. ''I can tell by the swings, by the takes. It's been a very different reaction from the hitters this year.''
Closer Jim Johnson was part of a strong effort by Oakland's bullpen. He allowed one hit in his inning of work and his ERA dropped to 3.00.
FLASHING THE LEATHER:
Chicago shortstop Darwin Barney, normally the team's second baseman, scooped up a low throw from second baseman Javier Baez for a force out in the fourth inning. Barney then started a double play in the fifth by getting to a ball headed up the middle.
Oakland second baseman Eric Sogard had to reach across his body to take a throw from catcher John Jaso with Christian Villanueva trying to steal second base in the second. Sogard got the throw on a bounce and reached back to apply the tag for the out. Jaso and Sogard later teamed up to nab Baez trying to steal second in the fourth inning.
CHICAGO: Shortstop Starlin Castro has a hamstring injury that has caused him to miss two weeks of spring games, but will run the bases Tuesday.
OAKLAND: Third baseman Josh Donaldson left Sunday's game with calf tightness and didn't play Monday. Melvin will hold him out until Wednesday. Outfielder Craig Gentry is working his way back from a back injury that has kept him out of spring training games but is taking batting practice.