In the seventh, Shaw extended Milwaukee's lead to 3-0 by hitting a long home run to right-center field.
The Brewers' other new corner infielder, first baseman Eric Thames, hit an RBI double and scored a run in the eighth.
Anderson worked around one walk and one hit -- a one-out single for Geovany Soto in the third inning -- in five scoreless frames, striking out six. His outing came one day after the Brewers announced the right-hander had won a spot in the starting rotation, and will pitch Thursday at home against the Rockies in the finale of a four-game series.