Beachy (3-1) yielded two runs on four hits and three walks. He struck out five in recording his fifth straight start without a loss.
Cristhian Martinez finished up with 2 2/3 frames of scoreless relief to earn his first save for the Braves, who scored 29 runs during their three-game sweep of the Rockies at Coors Field.
Freeman's first-inning blast gave Atlanta a quick 3-0 lead and Dan Uggla drove in a pair of runs, including a solo shot, in Atlanta's win.
Colorado starter Juan Nicasio (2-1) was tagged for six runs on eight hits before being yanked after five full innings.