Brooklyn lost key player James Harden after only four minutes with a hamstring problem and trailed by 10 points at half-time.
However, Irving's late three-pointer secured victory for the Nets.
"A lot of guys stepped up, especially our bench. They came in and made a difference," Irving said.
Harden was making his return on Monday after missing two games with tightness in his right hamstring and appeared to suffer the same problem against the Knicks.
The Nets are top of the Eastern Conference with 35 wins and 16 defeats.
Elsewhere, the Dallas Mavericks extended their winning streak to five matches with a 111-103 victory over the Utah Jazz.
Devin Booker scored a game-high 36 points to help the Phoenix Suns beat the Houston Rockets 133-130, while the Toronto Raptors claimed a 103-101 win over the Washington Wizards.