White Sox prospect Luis Alexander Basabe, the first batter Greene faced, hit a home run.
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Greene is 3-7 with a 4.69 ERA in 16 starts for Dayton. He has 80 strikeouts in 63 1/3 innings.
Trammell, of the Single-A Daytona Tortugas, hit a home run in the sixth inning to give the USA a 6-5 led. He tripled and scored in the eighth inning.
Trammell is hitting .295 with six home runs and 29 RBIs for Daytona.