Jermaine Mitchell's RBI single capped the eighth-inning rally. All three runs came against New York reliever Vic Black.
Dillon Gee pitched three-plus scoreless innings for New York, giving up five hits and striking out three without issuing a walk.
Scott Diamond fanned six in 3 2/3 innings for the Twins but allowed two runs on three hits and three walks.
Both teams went down in order in the ninth inning.