Freeman delivered a solo blast in the first inning and a three-run round-tripper in the seventh to cap the scoring, while McCann went deep in the fourth as the Braves pounded out 14 hits.
Alex Wood (1-2) recorded his first major-league win, limiting the Rockies to three runs on six hits over seven frames. The rookie left-hander issued one walk and struck out seven.
Colorado's Juan Nicasio (6-5) was scorched for eight runs on 10 hits over four full frames.
Nelson Arenado cracked a two-run homer for the Rockies.