Christmas had 14 points, 12 rebounds and seven blocks as Syracuse earned its 10th single-digit win despite shooting 35.2 percent. Jerami Grant had 12 points and 14 rebounds and Fair scored 11 points on 5-of-16 shooting.
The start of the game was pushed back four hours because of a snowstorm that wreaked havoc along the eastern seaboard. N.C. State did not land in Syracuse until Saturday afternoon. The team's Twitter account announced the Wolfpack's arrival at 3:07 p.m., seven minutes later than the original scheduled tip-off.
It turns out it was worth the wait, with a tight game leading to a frantic finish full of missed opportunities.
Ralston Turner missed a 3 for N.C. State with 2:45 left, and then Fair was off on a hook driving across the lane. After N.C. State's Anthony Barber hit the side of the backboard with a baseline jumper, Grant missed a spinning drive in the lane for Syracuse.
Tyler Ennis then fouled Turner while shooting a 3, and he made three free throws to give the Wolfpack a 55-53 lead with 62 seconds left.
Fair sank 1 of 2 foul shots with 41.4 seconds remaining and N.C. State's Desmond Lee then lost the ball out of bounds when he was double-teamed at midcourt.
Ennis negated that turnover with a charge, but the Wolfpack couldn't close it out. After a timeout with 18.3 seconds to go, Christmas stole the ball and Fair put the Orange in front when N.C. State was whistled for goaltending on his layup attempt.
T.J. Warren missed from the top of the key on one last try for N.C. State. Warren finished with 23 points, Kyle Washington had 14 and Turner 13 for the Wolfpack.
Despite its torrid season, Syracuse (25-0, 12-0) is clinging to a half-game lead over Virginia in the Atlantic Coast Conference. The Orange's start is the third-best in ACC history, behind only North Carolina State (27-0) in 1973 and North Carolina (32-0) in 1957.
North Carolina State (16-9, 6-6) was looking for its seventh win over the nation's No. 1 team. It got its last one just over a year ago, beating Duke 84-76.
The Wolfpack, who had won five of six, shot 39 percent (22 of 56) from the field.
Syracuse was coming off a dramatic last-second victory at No. 25 Pittsburgh on Wednesday night. Ennis hit a 3-pointer from 35 feet as time expired to lift the Orange to a 58-56 road win.
But the hostile Carrier Dome crowd of 31,572 didn't seem to faze the Wolfpack, who used Warren's big effort to hang right with Syracuse. He scored six straight points to start the second half and Washington's hook in the lane gave N.C. State a 34-30 lead.
Syracuse tied it at 34 on a slam by Christmas off an air ball by Fair from the right corner, and foul trouble on the Wolfpack hurt their chances. Grant's follow off a miss by Christmas gave Syracuse its first lead of the second half at 40-39 with 9:19 left.
There were seven ties and seven lead changes in the opening half, and the Wolfpack had the biggest advantage at 26-22 after a driving backdoor layup by Warren.
A spinning drive through the lane and layup by Fair and a fast-break dunk by Cooney off a Wolfpack turnover in the closing 2:11 made it 26-26 at the break.
It was Syracuse's fourth crowd of more than 30,000 this season. That's the most in any single season since Syracuse had six Carrier Dome crowds of more than 30,000 in 1990-91.