The Warriors held on for a 113-112 victory after Chris Bosh narrowly missed a layup as the buzzer sounded to allow Nelson to join Hall of Famer Lenny Wilkens at the top the list.
The 69-year-old Nelson celebrated on the sideline by jumping up and down alongside his team.
"You live for moments like that when the team wants something more than you do yourself," Nelson told reporters.
"What a game to tie the record. They are so happy that we got it together, as a group they were part of it."
A former player, Nelson is currently in his 31st season as a coach and is with his fourth different team.
The Warriors play at the Washington Wizards Tuesday when Nelson will have a chance to become the NBA's winningest coach.
(Reporting by Jahmal Corner in Los Angeles, Edited by Patrick Johnston)