The Yankees, however, lost the services of catcher Francisco Cervelli for at least six weeks after he was struck on the right hand by a foul tip from Rajai Davis in the game's first at-bat.
Team officials announced after the contest Cervelli had suffered a fracture in the hand and will require surgery.
In addition to that, New York starter Ivan Nova became ill and left the contest after two innings.
Phelps (1-1) came on in a 1-1 contest and gave up a run on two hits in his four innings of work. He left with New York holding a 4-3 lead and the Yankees held on to win their second in a row.
Mariano Rivera survived a bases-loaded jam in the ninth to claim his eighth save.
Reliever Brad Lincoln (0-1) gave up the go-ahead run in the fourth to take the loss.