The Wolfpack (9-1) led by eight points with 2:21 to play, but the Crimson Tide used a full court press and tough inside game to cut the lead to 65-64 with 25 seconds to play.
Atsur then hit his free throws - the Wolfpack's first of the game - for a 67-64 lead.
Alabama had a chance to tie the game when Ronald Steele put up a 3-pointer with 9 seconds to play. The ball bounced in and out of the basket and the Wolfpack held on for the win.
Chuck Davis scored 18 points for Alabama (5-4), mostly on layups and dunks. He scored his 1,000th career point early in the second half.
North Carolina State hit 11 3-pointers to just one for Alabama and used long range shots to stretch a 33-28 halftime lead to 51-41 with 10:58 to play.
The Crimson Tide tied the score several times in the second half, but each time the Wolfpack would go on a run sparked by 3-point shooting.
Atsur was 3-of-7 from behind the 3-point line, while Ilian Evtimov was 4-of-8 and also scored 15 points.
Cameron Bennerman added 14 points for the Wolfpack.
Chuck Davis scored 18 points for Alabama, mostly on layups and dunks. Davis scored his 1,000th career point early in the second half.