Gallinari, who made all seven of his free throw attempts in the second extra session, went 18-of-20 at the charity stripe for the game. He also had 11 rebounds.
Al Harrington contributed 24 points and 11 rebounds for the Nuggets, who have won four in a row.
Nene, who sat out Friday's win at Washington with a left heel strain, had 12 points and 13 rebounds in the win. Andre Miller ended with 14 points and 12 assists.
Carmelo Anthony, who spent seven-plus seasons in the Rocky Mountains before being dealt to the Knicks last February, had 25 points and 10 rebounds in New York's sixth straight defeat.