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.
Moore to attend retreat in to avoid Kutcher's wedding
'How to Train Your Dragon 2' releases 5-minute clip