Henson had 24 points and 10 rebounds, while Bullock added 15 points off the bench to spark the decisive spurt, helping the Tar Heels beat Long Beach State 84-78 on Saturday night.
Henson, a 6-foot-10 forward, has long been a defensive specialist who uses his long arms to pull down rebounds in traffic or swat away shots. But he made 12 of 17 shots for the Tar Heels (8-2), many on long jumpers. Meanwhile, Bullock scored eight in a row to help ignite a 13-2 run that gave North Carolina some breathing room against Casper Ware and the 49ers (4-5).
"I think it's just practicing all summer and then hitting the shots in the game is something that builds more confidence than anything," Henson said. "That's what I've been doing, hitting them in practice and building off of it and trying to become a complete player."
The junior got off to a fast start offensively, scoring 14 points on 7-for-9 shooting in the first half. But Henson made his biggest impact with his trademark defense by blocking layups -- on one, he grabbed the ball with two hands and snatched it away from T.J. Robinson -- on three separate possessions in the final 4 minutes. Long Beach State trailed by just six each time, the last coming when Henson blocked a shot from Ware in the lane with about 30 seconds left.
"I think he made some jump shots and yet I think that is fool's gold sometimes," coach Roy Williams said. "Our chances are better with Reggie or Harrison shooting and John rebounding as opposed to the opposite way. John took one down the stretch that I didn't want him to take, but in the second half, I thought he was so much more effective offensively than just shooting jump shots. He got involved defensively. He blocked some shots that were huge for us. John is just getting better and better."
To listen to Bullock, it was easy to see Henson's big performance coming. The two shoot together during pregame warm-ups, and both Henson and Bullock said Henson wasn't missing.
"When he hit those big shots at the top of the free-throw line to start the game off, I was like, 'Yeah, he's still feeling it from pregame,' " Bullock said.
Bullock did his best to keep pace. He hit two 3-pointers in his personal 8-0 run, the second snapping a 59-all tie and starting the run that ended with Henson's dunk off a feed from Bullock for a 72-61 lead with 8:41 left. It was his second straight game with 15 points.
"It's huge for us," Barnes said. "This whole year, we've been impressing on him to get in the gym and work on his game, and it was evident tonight by him coming off the bench and giving us the lift that we needed."
In addition, Kendall Marshall tied his career high with 16 assists for the Tar Heels, while Zeller's hook shot 90 seconds in gave him 1,000 career points.
While the Tar Heels led by as many as 11, they couldn't pull away and had to keep making plays into the final seconds to secure this one. Ware finished with a career-high 29 points for Long Beach State, which shot 47 percent, outrebounded the bigger Tar Heels and led 45-40 at halftime. Larry Anderson added 17 points and Robinson finished with 12.
"We don't feel like we're the Washington Generals," Long Beach State coach Dan Monson said. "We feel like we can play in these games. And yet sometimes you have to say that you got beat. I don't feel like we lost. I felt like they came in and had to beat us."
North Carolina shouldn't have had any thoughts of an easy victory coming in. Long Beach State tore up the Tar Heels' defense last December, cutting a 17-point second-half lead to two points with about 8 1/2 minutes left before UNC's offense carried the Tar Heels to a 96-91 victory. This season, the 49ers won at then-No. 9 Pittsburgh and cut a 19-point deficit to five with 3 minutes left in Tuesday's 88-80 loss at No. 13 Kansas.
In last year's meeting, Robinson scored a career-high 31 points and the 49ers shot 52 percent with10 3-pointers.
This time it was Ware, who had 14 points and hit four 3-pointers in the first six minutes. Then Anderson hit a pair of 3s in the final 90 seconds to give the 49ers a 45-40 lead at halftime.
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Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.