Mets starter Johan Santana held the Brewers to two runs on seven hits, while striking out 10 and walking one.
Nelson Figueroa (3-3) earned the win after pitching one-plus innings of relief.
Ryan Braun had three hits and an RBI, including a pair of doubles for Milwaukee.
Milwaukee starter Ben Sheets had to leave after the fifth inning with tightness in his left groin. The right-hander had a 1-0 lead at the time, having given up only two hits and one walk.
The Mets moved ahead with three runs in the eighth off Eric Gagne (4-3). Murphy doubled to left leading off and scored on Delgado's homer before Beltran scored on a double by Ryan Church.
Notable deaths of 2014 [PHOTOS]