Ty Lawson made a three-pointer with four seconds 116.
Lawson ended with 16 points, 13 assists and seven rebounds for the Nuggets, who started a season-long nine-game homestand on Monday. Arron Afflalo donated a career-high 32 points.
Kenneth Faried tallied a career-best 20 points and 12 boards for Denver, which has won four in a row. Al Harrington had 14 points and nine rebounds.
The Kings seemed to have the game wrapped up after Evans made two free throws with 28.1 seconds left in regulation for a 105-100 lead.
But Afflalo scored Denver's next eight points to force overtime. First, Afflalo made a finger roll layup to make it a three-point contest. After Isaiah Thomas made 1-of-2 from the line for the Kings, Afflalo made a three- pointer to cut the gap to one, 106-105, with 9.7 ticks remaining.
Thomas made two foul shots at the other end to make it a three-point game. Thornton then followed with a big mistake on the defensive end, fouling Afflalo on a three-pointer with 0.6 seconds to go. Afflalo made all three shots from the charity stripe to force overtime.
Sacramento jumped out to a 114-110 lead in the extra session, but the Nuggets had an answer once again. Afflalo's layup preceded Faried's layup and two free throws for a 116-114 edge with 1:10 to play.
Denver had a chance to build on its lead after Evans missed a three-pointer. However, Andre Miller was called for an offensive foul as he drove to the hoop and made a basket.
Evans tied the game on a layup with 24.9 seconds remaining. But Lawson responded with a three-pointer to give the home team a 119-116 lead with four ticks left on the clock.
Francisco Garcia's three-pointer was off the mark as time expired.
The Kings led by as many as 11 in the first half, but Afflalo scored eight straight points to make it 53-53 at the break.
Denver scored the final six points of the third quarter to take an 85-79 margin into the fourth.
The Kings used a 9-0 run early in the fourth to grab the lead. Thornton and Evans made back-to-back three-pointers with over a minute remaining, giving Sacramento a 103-98 edge.
Denver has won five straight over the Kings and seven consecutive at Pepsi Center in the series...Denver got leading scorer Danilo Gallinari and center Nene back. Gallinari missed 13 games with a left ankle sprain, while Nene sat out 10 contests with a calf injury. The Nuggets played without center Kosta Koufos (knee) and swingman Rudy Fernandez (back)...Sacramento fell to 2-10 in its last 12 games...Denver went 28-of-35 from the foul line...Keith Smart will be the head coach of the Kings beyond this season. The team announced Monday that it has exercised the option on Smart's contract for 2012-13.