"It feels good to get a win and get Larry his first win as head coach," Johnson said. "I know he's happy about it even though it's preseason."
Marvin Williams added 15 points, including 10 in the final three minutes of the second quarter, for the Hawks (1-3) at East Tennessee State University's MSHA Athletic Center.
Atlanta's starting five all played at least 25 minutes while only one Hornets starter played that much.
"As I told the guys before the game. It wasn't a concern about what New Orleans did," Drew said. "The focus of this game was on us and what we were to do on both ends of the floor. That's why I played a lot of our guys some pretty good minutes. We need to work on our game. We've got a ways to go."
Williams, who missed two games with flulike symptoms and was still listed as day-to-day, sparked an Atlanta comeback in the second quarter. He scored 10 points in the final 3:04 as the Hawks scored the last 13 points of the half to take a 43-37 lead.
Williams gave the Hawks their first lead with 1:04 left in the second quarter when he scored on a slash to the basket. He added two free throws, then capped the quarter with a 32-foot pullup jumper at the buzzer.
"He gave us a big spark," Johnson said. "That's what we need him to do all season. He's a big-time player. He's been great for us ever since we got him. I expect that from him."
New Orleans tied it at 56 with 2:34 left in the third quarter with four free throws, two on technical fouls against Atlanta's Josh Powell and Josh Smith. Smith then scored six of Atlanta's next eight points as the Hawks regained the lead for good.
Marco Belinelli led New Orleans (1-4) with 13 points. Willie Green and Quincy Pondexter each had 10.
"Guys are playing the defense we want," Hawks coach Monty Williams said. "We held that team to 84 points. I was encouraged. We didn't play a starter in the second half other than Marco."
Hornets point guard Chris Paul didn't play after the first quarter. His three-point effort was his lowest output of the preseason. Hornets forward David West missed his fourth consecutive preseason game because of a sprained right wrist. Jason Smith made his third start in West's absence.