New York let all of a 23-point lead get away and made only 21 percent of its shots in the fourth quarter, but managed to hold on for its sixth victory of the season.
The Knicks put together a 19-0 run in the first half to seemingly take charge, but the Bulls came all the way back to tie it at 74-74 on Joakim Noah's tip-in with 3:37 to play.
A jumper by Amare Stoudemire with 2:38 left put the Knicks back in front for good and they relied on Anthony's free throw shooting toe rest of the way.
Anthony scored 30 points and Stoudemire had 14. They were the only Knicks in double figures.
Chicago, which has dropped three in a row and nine of 11, was led by Mike Dunleavy's 20 points.
New York played without point guard Raymond Felton, who sat out with a sore hamstring.