It was a thrilling finish to a game that saw Harrison Barnes score 30 points for the Kings.
The Nuggets head coach Michael Malone praised the Kings' comeback.
"They played well, give them credit. They played good defence and turned up the pressure and we didn't handle it well," Malone told reporters after the game.
Despite the loss, the Nuggets (13-4) are still in second place in the Western Conference, while the win sees the Kings improve to 8-10 and in ninth place in the West.
Perhaps more importantly to the 76ers, Ben Simmons had three steals in the final 13.9 seconds
Philadelphia have now won three straight and lie in sixth spot in the Eastern Conference, one place ahead of Indiana.
In Milwaukee, the Bucks trounced the Charlotte Hornets 137-96 in a game the home side took command of early on and never trailed.
Giannis Antetokounmpo got the biggest individual haul with 26 points, and gave his enormous game shoes to a fan afterwards.
The Bucks have now won 11 straight and remain on top in the East, while the Hornets drop to ninth.
The win moves the Rockets (13-6) up to fourth in the West, while the hapless Hawks, who have now lost 10 straight, remain rooted to the bottom in the East.