Nelson, who has also coached the Dallas Mavericks, New York Knicks and Milwaukee Bucks, surpassed Hall of Famer Lenny Wilkens's mark with the win, prompting his team to douse their coach in water and soda.
"It's such a great feeling," Nelson told reporters after watching Anthony Tolliver spark the victory with 34 points.
"This is probably why we end up coaching, for moments like this."
Coaching in his 31st season, Nelson has stood the test of time with his unorthodox style and knack for putting together unconventional lineups who play entertaining basketball.
Though he has led four teams during his career, Nelson has never reached an NBA Finals.
(Reporting by Jahmal Corner in Los Angeles, editing by Nick Mulvenney)