The Marlins grabbed the lead in the eighth with three consecutive two-out singles, breaking up Dillon Gee's shutout bid in a game that took only 1 hour, 58 minutes.
It was the fastest nine-inning game in the majors since the Padres and Astros also finished in 1:58 on June 27, 2012, according to STATS.
Jarred Cosart matched Gee by allowing only two hits in eight scoreless innings. But the Mets rallied against closer Steve Cishek (0-1), who blew a save for the second time in three chances this year.
The Mets (15-5) won with five hits. They have the best record in the majors and improved to 5-0 against Miami.
The second baseman came into the game batting only .169, though he did have a pair of RBI doubles in Sunday night's loss at Yankee Stadium.
Jeurys Familiar pitched a perfect ninth for his major league-leading ninth save in as many chances, completing a six-hitter and breaking the team record for saves in April. Familia was helped by Murphy, who made an acrobatic play to rob Michael Morse of a hit.
Gee threw 24 first-pitch strikes and took a three-hit shutout into the eighth. He retired 14 batters in a row before pinch-hitter Justin Bour singled with two outs. Dee Gordon also singled, and pinch-runner Reid Brignac slid home safely on Martin Prado's single.
Carlos Torres (1-0) retired Giancarlo Stanton on a popup with two on to end the inning.
Mets: Former closer Bobby Parnell (Tommy John surgery) is scheduled to throw on flat ground Thursday. He was shut down last week because of forearm soreness but said no structural problems were found.
RHP Rafael Montero (0-1, 4.15 ERA) is scheduled to make a spot start Tuesday night against Miami, giving the Mets' rotation an extra day of rest. Manager Terry Collins said he's not looking to make any changes in the rotation, but will likely use a spot starter again at some point because the Mets want to limit ace Matt Harvey and 41-year-old Bartolo Colon to 30 starts each. RHP David Phelps (1-0, 3.55) will start for the Marlins.