Jimmy Rollins drove in three runs for the Phillies and Roy Oswalt had an RBI single to go with six effective innings on the mound. With runners at the corners, Ryan Madson got Murphy to ground into a game-ending double play.
Brown entered as a pinch-hitter in the eighth and singled to start the tying rally. He stole a base and scored twice, helping the NL East-leading Phillies get off to a good start on a nine-game trip.
Philadelphia had dropped its last four road games since a May 13 victory at Atlanta.
Justin Turner had a career-high four hits for the streaky Mets, who have dropped five of six after winning 10 of 14. Still missing injured boppers David Wright and Ike Davis, they tried to mount a rally in the ninth but fell short.
Jose Reyes scored on an error by center fielder Michael Martinez, Philadelphia's third of the game, to make it 6-4. Jason Bay's single put runners at the corners, but Murphy couldn't come through.
Antonio Bastardo (3-0) worked a hitless eighth and Madson, filling in for injured closer Brad Lidge, earned his 10th save in 10 chances.
Mets starter Chris Capuano struck out eight in six strong innings and Turner's RBI double gave New York a 3-2 lead in the seventh. Jason Isringhausen, however, couldn't hold it.
Brown opened the eighth with a single and stole second before scoring on Rollins' double.
Carlos Ruiz and pinch-hitter Ross Gload singled with one out in the ninth against Rodriguez (1-1), who began the night with a scoreless streak of 19 2-3 innings - the longest active run in the majors.
Brown hit a grounder that stayed down on Murphy, who might have had a shot at an inning-ending double play. But he started to whirl toward second without the ball, and it scooted into right field for an RBI single.
Rollins followed with a sacrifice fly and Placido Polanco added an RBI infield single to make it 6-3.
New York opened a 10-game homestand, its first game at Citi Field since owner Fred Wilpon's critical comments about Wright, Reyes and Carlos Beltran were published.
NOTES: CF Angel Pagan returned to the Mets' lineup after missing more than a month with an injury to his rib cage. He had two hits and a stolen base. ... Phillies CF Shane Victorino, on the DL, is set to begin a minor league rehab assignment Saturday and could be back next Friday.
