Seth Lugo (6-5) was charged with eight runs, seven earned, with nine hits and a walk over three innings.
The Mets took a 5-3 lead in the third inning on back-to-back home runs by Dominic Smith and Travis d’Arnaud.
Consecutive R.B.I. doubles by Jon Jay, Bryant and Rizzo highlighted a five-run fourth inning as the Cubs rallied with nine straight runs.
One night after knocking in six off the bench, Albert Almora Jr. had a two-run, pinch-hit double in the sixth. Heyward added a three-run homer later in the inning to make the score 14-5.
Tomas Nido had his first career hit and R.B.I. for the Mets in the ninth.
Shortstop Amed Rosario left the game in the fifth inning with a tight hip flexor. … Travis D’Arnaud left the game in the sixth inning with a twisted right knee.