Baker has been out with elbow tendinitis that flared up in a "B'' game on March 10. On Monday, he gave up seven runs and seven hits in 2 2-3 innings.
Zobrist went 3 for 3 to spark the Rays' 14-hit attack after the team came into the game with a .222 batting average in spring training.
Jeff Niemann, competing for the fifth spot in the Rays' rotation, gave up two runs on six hits through five innings, striking out five.
Backup catcher Ryan Doumit, who played in the outfield, hit his first home run for the Twins since being acquired in the offseason from the Pirates.