Murphy knocked in four runs and David Wright had three hits, two RBI and two runs scored for the Mets, who have won three in a row overall.
Zack Wheeler gave up five runs on seven hits and six walks in 4 1/3 innings for the Mets and Daisuke Matsuzaka (1-0) earned the win with 3 2/3 innings of relief work.
The Mets won the opener of the four-game series 9-7 on Monday night at Yankee Stadium. The last two games of the home-and-home will be played at Citi Field.
Brian McCann hit a two-run homer and Yangervis Solarte added a solo shot for the Yankees, who have lost a season-high four in a row. McCann had three hits and three RBI.
Nuno (1-1) gave up seven runs -- five earned -- on four hits and four walks in just 3 1/3 innings. The lefty's ERA climbed nearly a full point to 6.43.
Yankees outfielder Carlos Beltran missed the game after being diagnosed with a bone spur in his right elbow. Beltran left Monday's game for a pinch-hitter in the seventh inning. The team will wait to see if a cortisone shot works before deciding if surgery is necessary.
The Mets had two four-run rallies in the first five innings.
Granderson's three-run blast to right field punctuated a first-inning flurry and Murphy's three-run shot high off the netting on the right-field foul pole to make it 11-4 in the fifth.
Wright had an RBI single in the first and a leadoff double in the third, scoring a run. He hit an RBI single in a two-run fourth after Alfredo Aceves relieved Nuno.
Wheeler labored, too, putting the first two Yankees batters on base in the first, though the damage could have been worse. Jacoby Ellsbury hit into a double play before Mark Teixeira's RBI single and McCann's two-run homer to right got the Yankees within 4-3.
The right-hander gave up an RBI single to Brett Gardner in the fourth but escaped any more trouble when Derek Jeter grounded into an inning-ending double play. He came out after Alfonso Soriano's RBI single in the fifth, which pulled the Yankees within 11-5.
Solarte led off the eighth with a homer off Matsuzaka and Lucas Duda hit an RBI double in the ninth for the Mets.
The game was almost four-hours old when members of the grounds crew were called out in the ninth inning after Mets reliever Jeurys Familia was having trouble throwing off the mound. They put down dirt in front of the rubber and raked and watered it.
Familia walked two and gave up an RBI single to McCann for the final margin.