Giambi hit a two-run double and Atkins a two-run homer, both in Colorado's five-run bottom of the third.
Seth Smith added an RBI single for the Rockies, who made the most of seven hits in their seventh win in a row.
The victory was tempered by the loss of starter Jose Contreras, who was injured while running out a third-inning ground ball.
Contreras gave up a run and four hits in three innings with three walks and five strikeouts.
The winner was reliever Juan Rincon (3-2).
Brandon Phillips had three hits and one RBI and Joey Votto added two his for the Reds, who had won seven straight before the sweep.
The losing pitcher was starter Kip Wells (1-4).