Wade Miley worked eight innings for the first time in his 16 career starts while limiting the Rockies to three hits.
Goldschmidt had an RBI double in both the first and third innings and hit a solo homer in the seventh. He ran his hitting streak to 14 games and has had multiple hits in five of his last seven contests.
Miley (7-2) gave up a run without a walk and struck out five to get the victory.
Josh Outman (0-2) made his second start of the year and was roughed up for five runs on seven hits in three innings to take the loss.
Colorado has dropped the first two games of the series after winning seven out of eight.