The Mets led 4-0 after three innings but the Dodgers scored twice in the sixth before Ethier's home run forced extra innings.
Yasiel Puig and Gonzalez hit consecutive doubles in the 12th off reliever Pedro Feliciano (0-1) that capped the comeback and gave the Dodgers an eighth consecutive win.
Paco Rodriguez (3-2) collected the win with 1 1/3 innings of one-hit relief.
Andrew Brown had a second-inning RBI double and Marion Byrd hit a three-run home run the next inning in building the 4-0 Mets lead.
Los Angeles didn't have another base runner until the ninth when Mark Ellis led off with a single off New York closer LaTroy Hawkins. After an out, Ethier hit a drive the opposite way into the left-field seats that tied the score.
Puig legged out a double on a grounder into shallow center field and Gonzalez lined the next pitch down the left-field line and Puig scored without a throw.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged