Anderson (1-0), who spent 14 months mending from Tommy John surgery, went seven innings, allowing one run on four hits with six strikeouts and no walks.
He benefited from a triple play in the fifth inning when Trevor Plouffe grounded to third with runners on first and second. Josh Donaldson stepped on third to start a 5-4-3 triple play.
Donaldson had two hits and an RBI for the A's, who have won five of their last six games. Seth Smith had two hits and scored twice.
Cole De Vries (2-5) allowed two runs on six hits over 5 2/3 innings in Minnesota's 10th loss in 12 games.
Ben Revere led off the game with a single and then scored the Twins only run on a wild pitch after stealing second and advancing to third on a groundout.
Disney's 'Jessie' to feature network's first engagement
Rosie O'Donnell unveils nearly 50-pound weight loss