Baker (6-5) scattered six hits and a walk in the Twins' second straight win after losing six in a row. Baker struck out nine.
Matt Capps completed the shutout for his 13th save this season.
Rubby De La Rosa (3-3) absorbed the loss despite allowing just one run on six hits and two walks through seven innings.
Matt Kemp got the only extra-base hit for the Dodgers, a double.
Los Angeles has now lost five of its last seven games.
Notable deaths of 2014 [PHOTOS]