C.J. Williams and Richard Howell each scored 10 points for the Wolfpack (16-7, 5-3 Atlantic Coast Conference). N.C. State has won 10 of its last 13. Howell also grabbed eight boards.
Matt Humphrey led Boston College (7-15, 2-6) with 15 points. The Eagles lost their fifth straight.
Wood also hit 5 of 5 free throws and has made 63 straight dating back to last season, extending his school record.
Leslie broke a 44-all tie with a jumper from the top of the key and then hit two free throws, pushing the Wolfpack ahead by four with 3:57 left. They had a chance to go up by six, but Howell missed a breakaway layup after stealing the ball.
But Howell made up for it about a minute later when he scored on a baseline drive, making it 50-46 with 2:07 to go. He did miss the free throw after he was fouled on the play.
Wood hit four free throw attempts in the final 1:38 to seal it.
The Eagles had just two baskets in the final 5:17, both coming after they were down eight points in the final minute.
N.C. State led 25-23 at the half, but BC grabbed the lead on Jackson's four-point play when he nailed a 3 on the right wing and hit the free throw. It was the Eagles' first lead since 3 1/2 minutes into the game.
The lead then switched hands five times over the next 13 1/2 minutes. Neither team held more than a four-point advantage before Ryan Anderson banked in a one-hander from the lane to push N.C. State back in front, 42-41, with 6:22 to play. Wood had just given the Wolfpack the lead 35 seconds earlier with his third 3-pointer of the game, this one coming from the right corner.
The Eagles slowed the ball down and used nearly the entire shot clock on most of their possessions. At times, BC coach Steve Donahue was visibly upset even when his players took wide-open jumpers.
In the first half, N.C. State had a six-point lead twice, but the Eagles scored six straight to tie the game at 19 on Anderson's short flip in the lane. N.C. State then scored six of the next eight points en route to its halftime edge.
It was the Wolfpack's lowest first half scoring total of the season and matched BC's fewest points, done three other times.
BC forward Patrick Heckmann missed his second straight game due to an illness, but was on the bench for this one.