Gary Gaetti hit a grand slam in the first and Kent Hrbek had a two-run homer in a game New York played under protest, contending conditions at Minneapolis' Metrodome are not up to major league standards.
Winner Mike Smithson (4-2) gave up eight hits in 8 2/3 innings and Pete Filson got the final out for his first save. It was the Twins' 13th victory in 15 games.
With one out in the first, Minnesota's Mickey Hatcher singled and scored on Hrbek's double. Starter Joe Cowley (0-2) walked Mike Stenhouse and Roy Smalley to load the bases. Gaetti then hit his third career grand slam and fifth homer of the season, a 431-foot shot to left.
The Yankess pulled to 5-3 in the second on Rickey Henderson's RBI single and Ken Griffey's two-run double.
Hrbek's homer, a 400-foot drive to left center in the fourth, followed a walk to Dave Meier and gave the Twins a 7-3 lead.
The Yankees, who lost by 8-6 Tuesday night to the Twins after misjudging several fly balls, contended the lighting in the Metrodome was inadequate.
Twins Manager Billy Gardner said the team plans to install about $100,000 worth of lighting in an effort to eliminate shadows, but added, "It's a farce. Every ball club coming in here could protest but we play 81 games a year here."