Josh Satin contributed two hits and an RBI, and Murphy scored two runs for the Mets, who ended a three-game losing streak.
Scott Atchison (3-1) earned the win after a perfect inning in relief and Gonzalez Germen recorded his first career save after a pair of scoreless innings.
Mets starter Zack Wheeler gave up one run on seven hits while striking out a career-high 12 batters over six innings.
Luke Gregerson (5-7) was saddled with the loss after giving up Byrd's double.
Notable deaths of 2014 [PHOTOS]
LeBron James reveals his new Nike shoes