Durant passed Spencer Haywood's mark from the 1972-1973 season with Seattle.
Oklahoma City coach Scott Brooks joked before the game that he might try to keep Durant from hitting the mark because of his admiration for Haywood. But as the NBA-worst Nets (7-58) climbed back in the game in the fourth quarter, Durant had to do the extra lifting.
"Durant eventually got himself going," Nets coach Kiki Vandeweghe said. "He is a terrific player, top five player in this league. Even though we were hitting him off of somebody every time, he still got his points."
Durant finished off his record night with two late free throws to clinch the Thunder's 40th victory of the season and 16th in their last 19 games.
The Thunder (40-24) led by 15 points with 6:36 remaining, but when Oklahoma City called a timeout with just under two minutes remaining, New Jersey was back within seven. New Jersey trimmed the lead to four on a 3-pointer by Terrence Williams.
Oklahoma City committed four turnovers in the final two minutes and Russell Westbrook had to hit two free throws with 6.3 seconds left to preserve the victory and pull the Thunder within 1 1/2 games of Utah for the fourth seed in the Western Conference standings. The teams square off Sunday.
Durant went 5 for 12 in the first half, when teammate Jeff Green scored 20 of his season-high 27 points. Green knocked down two early 3-pointers to open the court.
"They had to honor that," he said. "Once I made a couple shots, they had to step out. And when they did step out I was able to attack the rim.
"It started on the inside. Once it started inside, I hit one 3 and then I hit another and then everything opened up."
Westbrook finished with 11 points and 10 assists, while Nick Collison came off the bench to add 10 points and nine rebounds. Former Nets center Nenad Krstic scored 10 points for the Thunder.
"The guys are learning that we aren't good enough to play without a real high level of effort for 48 minutes," Vandeweghe said. "When we have a slight letdown, that's when teams pull away from us. That's happened a couple of times at the beginning of the game in the first quarter and sometimes in the third quarter."
Oklahoma City went on an 18-2 run in the first quarter and scored 13 fast-break points in the first 12 minutes. The Thunder stretched the lead to 10 at halftime and led by as many as 16 points in the second half.
Oklahoma City was playing without key reserve James Harden, who strained his right hamstring against New Orleans on Wednesday. Brooks said before the game that Harden could miss up to four weeks.
Kyle Weaver, recalled by the Thunder from Tulsa of the NBA D-League after Harden's injury, checked into the game late in the first quarter and finished with no points in 10 minutes. With an attendance of 18,203, Oklahoma City passed last season's mark of 18 sellouts in only 33 games. The Thunder have nine home games remaining on the schedule.