Garnett, 39, eclipsed the record early in the first quarter and was given a warm ovation by the crowd at Pepsi Center. He finished the game with four defensive boards to give him 11,409 for his career, three ahead of Malone.
Defensive rebounds has been an NBA stat since the 1973-74 season.
Garnett's career rebound total, including defensive and offensive boards, stands at 14,612, good for ninth all-time. Among active players, he trails only the San Antonio Spurs' Tim Duncan, who has 14,828.
The Associated Press contributed to this report.