D'Angelo Russell exploded for 39 points, the most by an NBA rookie this season, hitting eight of his 12 three-point attempts.
Nets center Brook Lopez fouled out with just over two minutes left in the game, but Brooklyn managed to close the gap to 95-94 with 1:50 on the clock.
Jordan Clarkson, who finished with 16 points, seven rebounds and seven assists, stemmed the tide with a layup, and Russell followed with a three-pointer.
Former Lakers guard Wayne Ellington responded with a three, but Russell responded in kind, giving the Lakers a six-point lead with 30 seconds left in the game.
Russell finished the night with a pair of free throws. For the game he made 14 of 21 shots from the field and three of five from the line.
The Nets shot 43.8% from the field, 27.8% from three-point range (five for 18) and 66.7% from the line (18 for 27). The Lakers hit 49.4%, 42.3% (11 for 26) and 66.7% (14 for 21), respectively.
Julius Randle and Roy Hibbert each scored 14. Randle also collected 13 rebounds.
The Lakers (12-49) play again Wednesday, visiting the Denver Nuggets (23-37). The Nets (17-44) will also make the trek to Denver, where they play Friday night.
Lou Williams was limited to 10 minutes because of a moderately strained left hamstring. He'll miss the Lakers' trip to Denver.
Kobe Bryant sat out his second straight game to rest a sore right shoulder. He's expected to travel with the Lakers to make his final career appearance in Denver. Rookie Anthony Brown started in his stead, scoring just two points in 26 minutes.