The center said it was a "special moment" when he passed Kobe Bryant's 81-point tally, set in 2006.
Wilt Chamberlain's record of 100 points has stood since 1962.
Adebayo scored 36 of 43 free-throws - records for the most free-throws attempted and most free-throws made - at Kaseya Center in Miami.
"It's Wilt, me, then Kobe, which sounds crazy," he said.
The 28-year-old described it as a "special moment" and said he "really got emotional" when he realised the scale of his achievement.
"I wish I could relive it twice," Adebayo said.
Paying tribute to his family and trainers, he said: "They've seen me at the lowest, at the bottom of the bottom, trying to figure out how to really pick myself up.
"To have this moment and share it with all them, it's a pretty emotional moment."
The Los Angeles Lakers beat the Minnesota Timberwolves 120-106 at home thanks to Luka Doncic's 31 points, 11 rebounds and 11 assists.
The Lakers climbed to fourth in the Western Conference, ahead of the Timberwolves on a tie-breaker as they both have 40-25 records.
Eastern Conference leaders the Detroit Pistons moved to 46-18 with a 138-100 win at the Brooklyn Nets as Jalen Duren scored 26 points.
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Adebayo on scoring second-most points in NBA history
