Anthony "Cat" Barber had 17 points on 3-of-11 shooting with a career-high 12 rebounds, and freshman Maverick Rowan added 15 points for the Wolfpack (1-1).
They bounced back from a surprisingly one-sided loss to William & Mary two nights earlier in the opener by shooting 51 percent — nearly 59 percent after halftime. They never trailed but couldn't pull away until early in the second half.
Taishaun Johnson had 18 points for the Jaguars (1-1), who shot just 31.5 percent.
Abdul-Malik Abu added 14 points for N.C. State, which broke this one open by scoring on seven straight trips downcourt in the second half. Martin — who scored a career-best 21 points against the Tribe — played a central role in that spurt.
He sandwiched a pair of 3-pointers around a stickback of Abdul-Malik Abu's missed jumper. BeeJay Anya's putback dunk two possessions later made it 60-44 with 11 minutes to play.
That put the Wolfpack well on their way to the win and helped them avoid their first 0-2 start since the 1993-94 team opened with consecutive losses to Weber State and Wisconsin-Green Bay at the Great Alaska Shootout.
They also wanted to prove they could win without shooting guard Terry Henderson, the latest in a series of high-scoring guards who transferred to N.C. State. He will miss at least six weeks after suffering an ankle injury against William & Mary.
The Wolfpack trailed by 23 in that 85-68 defeat, and for a while, there was a lingering sense that they were in for a fight against a team picked to finish seventh in the Sun Belt.
This was a four-point game in the final minute of the first half — when Don MuepoKelly's putback dunk with about 30 seconds left made it 38-34. N.C. State didn't take its first double-figure lead until Barber's free throw with 18:37 to play pushed it to 44-34.
South Alabama: The Jaguars were denied their first win over an Atlantic Coast Conference team since the 2012-13 opener, when they knocked off Florida State.
N.C. State: Rowan replaced Henderson in the starting lineup. The Wolfpack went with just seven players for most of the night, and their eighth man — swingman Shaun Kirk — entered with 2:18 remaining and N.C. State up by 19.
South Alabama is at No. 21 LSU on Thursday night.
N.C. State hosts IUPUI on Wednesday night.