Devon Bookert added 18 points for the Seminoles (11-5, 1-3), who led just about all night but still had to keep coming up with some timely baskets to stay in control.
Both teams entered this one at 0-3 in the Atlantic Coast Conference for the first time since the 2006-07 season, with each staring at its first 0-4 start in more than a decade.
But Beasley, Bookert and freshman Dwayne Bacon each had key second-half baskets that helped FSU finally break through.
Now it’s the Wolfpack (10-7, 0-4) still searching for a first league win with a daunting schedule – at No. 5 North Carolina, at No. 20 Pittsburgh, home against No. 9 Duke – looming in the next 10 days.
Abdul-Malik Abu scored a career-high 21 points to go with 13 rebounds and a career-best six assists to lead N.C. State, while Anthony “Cat” Barber – the ACC’s leading scorer – finished with 16 points.
N.C. State shot 38 percent and went 7 for 26 (27 percent) from 3-point range, but hung around by making 23 of 32 free throws.
N.C. State made its final push with freshman Maverick Rowan shaking off a game’s worth of shooting struggles to bury two straight 3-pointers – one immediately after an FSU turnover – to bring the Wolfpack within 79-76 with 37.9 seconds left.
But Xavier Rathan-Mayes answered with two free throws, Rowan and Barber each missed 3s on the ensuing possession and FSU hit its last four free throws to hold on for a road win.