The Braves scored seven times in the second inning, staking an early 9-0 lead.
Freeman also had a two-run double in the first while Bourn finished 3-for-5 with two runs scored for Atlanta, which won for the 14th time in 17 contests.
Medlen (3-1) yielded only one run on five hits over 6 1/3 frames, walking one and striking out seven.
Mets starter Johan Santana (6-8) was pounded in his return from a three-week stint on the disabled list with a right ankle injury. The left-hander lasted only 1 1/3 innings, allowing eight runs on eight hits.
Ruben Tejada went 2-for-4 with an RBI for the Mets.