Beachy gave up five hits and no walks. He posted a 0.90 ERA for the spring to beat out Mike Minor and Rodrigo Lopez for the fifth spot in the Braves' rotation.
The Twins scored two runs in the eighth off Lopez. Jason Kubel drove in Jason Repko with a double, and Kubel scored on Brian Dinkelman's single.
Baker gave up three hits with a walk in five innings.
Lopez, who is headed for Triple-A Gwinnett, pitched five innings, giving up three hits and two runs.
Minnesota finished the spring 20-12. Atlanta was 17-13.
The Braves begin the regular season at the Washington Nationals on Thursday afternoon.