Medlen (3-6) notched his second straight start without allowing an earned run, shutting down the Dodgers on five hits. The right-hander walked one and struck out six, throwing 81-of-116 pitches for strikes.
Medlen's solo shot in the fifth gave the Braves a 2-0 lead after Dan Uggla had gone deep earlier in the frame.
Craig Kimbrel hurled a 1-2-3 ninth for his 18th save as the National League East-leading Braves bested the Dodgers after two consecutive losses.
The loss was hung on Los Angeles starter Stephen Fife (1-1), who allowed two runs on nine hits over 6 2/3 frames.
Hanley Ramirez drove in the Dodgers' only run.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys