Brook Lopez's bucket inside gave New Jersey a 100-99 lead, then Harris took Larry Hughes' turnover the other way for an uncontested layup with none of the Knicks scurrying back on defense, making it a three-point game with 1:15 to go.
Harris and Bobby Simmons each added a pair of free throws in the final seconds after empty New York possessions.
David Lee had 19 points and 14 rebounds for the Knicks, who opened a five-game trip with their fifth loss in six games. Nate Robinson scored 17 points and fellow reserve Danilo Gallinari added 15.
Lopez finished with 16 points in the final game before both teams left the New York area for a while. The Knicks move on to Milwaukee, while the Nets now face their own five-game trip, with the first four out West before closing at New York on March 18 - the Knicks' next home game.
The Knicks might be out the playoff race by then. They are 7-22 on the road and fell 3½ games behind eighth-place Chicago for the final spot in the Eastern Conference.
New Jersey is in better shape, a game back of the Bulls.
Carter limped off after banging knees with Gallinari trying to fight through a screen with 4:39 remaining. Hughes hit a wide-open 3-pointer after Carter fell to tie it at 96, and Gallinari's 3 gave the Knicks their last lead at 99-98 with 2:49 remaining.
The Knicks made 11 of 17 shots in the first quarter (65 percent), when there were 12 lead changes and seven ties, and were ahead 30-27 going to the second. New York held a narrow lead for most of the second quarter, then took a 57-53 halftime lead after Chris Duhon made two 3-pointers in the final 33 seconds.
New York pushed the lead to nine early in the third, but the Nets went ahead with a late 10-2 run and brought a 79-77 edge to the fourth.
Notes: Knicks center Eddy Curry, who has missed all but 3 minutes of the season because of knee problems, worked out before the game and said he was feeling good and his swelling was down. However, he said he still won't be ready to play until he has some more practice. "Right now, this second, I don't feel like I can go out there and play," he said before the game. "But keep working hard, go in tomorrow early, get some extra work done, see what happens. See if I can get in a game on this road trip if the opportunity presents itself." ... The Nets celebrated "An Evening of Chinese Culture." Starting lineups were announced in Mandarin, and China's Yi Jianlian thanked the crowd before the tip.
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