LaVine scored 14 points in his first game in 11 months, rookie Lauri Marrkanen added 19 points and the Bulls beat the Detroit Pistons 107-105 on Saturday night.
Chicago made 17 3-pointers and held off several late charges by the Pistons to win for the 13th time in its last 20 games.
LaVine was making his Bulls debut after being acquired from Minnesota in the Jimmy Butler trade. LaVine, who last season averaged 18.9 points in 47 contests, hadn't played since he suffered a torn ACL against Detroit on Feb. 3.
"It actually felt really good," LaVine said. "It wasn't that fast paced. I was tired, but it wasn't that fast. I was relaxed."
Coming off a career-high, 33-point effort on Wednesday, Markkanen hit a 17-foot shot with 1:08 to go to give the Bulls a 106-105 lead. The game featured 23 lead changes and seven ties.
Chicago then survived four late shot attempts by Detroit, including a missed layup by Drummond with 38 seconds left.
"We just didn't close," Pistons coach Stan Van Gundy said. "In the first half, we just didn't close. Our guys are not closing out. Period."
It was the second straight close victory for the Bulls after an overtime win at New York on Wednesday.
"It means a lot and it's especially nice to have Zach back," Markkanen said. "Just to see how he moves and how quick he is, how well he can shoot the ball. All around he's a great player and he's going to bring a lot to the team."
With LaVine on the court, the Bulls reached 100 points for the 17th time in 20 games after reaching the mark only eight times in their first 23 contests.
LaVine made his first shot, a 27-footer from the right of the key, before he assisted Robin Lopez's basket inside. The fourth-year guard followed with an easy 15-footer at the 8:12 mark in the first quarter to give Chicago an early 12-11 lead. LaVine made 5 of 9 shots and finished with two assists.
"(LaVine is) a very smooth player and has a lot of confidence to rise up on his first shot and knock down a 3," Chicago coach Fred Hoiberg said. "(That) shows you that he's just been itching for this moment to get out there and back on the floor with his teammates."
Eight of Drummond's 15 rebounds were on the offensive end, which helped Detroit to a 30-6 advantage in second-chance points.
Pistons: Forward Stanley Johnson sat out with a sore right hip flexor after missing practice on Friday. "They're not really seeing any structural things, he's just really tight," Van Gundy said. "Problem's moving in one direction. I don't know if it's necessarily a pain thing. It's his ability, in his mind, at least, to move."
Bulls: Connected on 17 3-point tries to match the franchise record with a seventh consecutive game with at least 10 3-pointers made. Chicago made its first six tries from beyond the arc, including all three by Markkanen, to equal the previous stretch from March 21-April 2, 2017.
Upset he missed a wide-open, 3-pointer to give the Bulls the lead, Hoiberg said Markkanen apologized to his teammates in the huddle. Hoiberg drew up the next play for Markkanen, who hit the go-ahead shot.
"Robin (Lopez) set a great screen to get him open," Hoiberg said. "(Markkanen) had no hesitation, he rose up and knocked it down. To be that calm as a 20-year-old rookie is a great sign for him."
LaVine on his return: "Not really butterflies, just anxious. It's just what I love to do. It's one of the best feelings to go out there, play in front of 20,000-plus people, your teammates supporting you, coaches that support you, medical staff, your family, a lot of people having your back."
Pistons: Host Charlotte on Monday.
Bulls: Host Miami on Monday.
More AP NBA: https://apnews.com/tag/NBAbasketball
Andrew Bogut back but Warriors woes return
The second coming of Andrew Bogut wasn't enough for the Warriors as they fell to a red-hot Spurs outfit in San Antonio.
Rivers on new contract: Wanted to end 'noise' of leaving Clippers
Doc Rivers says he and the Clippers didn't want to make a "big deal" of his contract extension, but had to announce it to end speculation of him leaving.
Nets shower Hollis-Jefferson after scoring game winner
The Nets celebrate after shocking the Kings with a 25-point comeback and Rondae Hollis-Jefferson breaks it all down.