Kenyon Martin had 24 points and 12 rebounds and Chauncey Billups had 23 points for the Nuggets, who improved to 3-0 in overtime this season and averted being swept in their three-game season series with the Kings.
The Nuggets, playing a fifth straight game without All-Star forward Carmelo Anthony (ankle) also got 15 points from Ty Lawson, 14 points from Nene and Afflalo had six of his 12 points in the extra period.
Spencer Hawes had 23 points and Kevin Martin had 22 for Sacramento, which lost for the third time in four OT games. The Kings lost their 10th road game in a row.
Hawes hit a 3-pointer to give the Kings a 109-107 lead with 1:36 left in overtime but Nene tied it eight seconds later with a layup. A Sacramento turnover -- Kevin Martin lost the ball at the Kings' end -- opened the door to Denver's decisive final possession. Afflalo hit the shot following a jump ball won by the Nuggets.
After a Denver turnover on a bad pass by Nene, Sacramento evened the score at 99-99 on Hawes' tip-in with 27.9 seconds remaining in the fourth quarter.
Both teams had a chance to win in regulation. Billups' missed a 3-point shot with just under 3 seconds remaining and Hawes missed a jumper at the buzzer, sending the game into overtime.
Consecutive baskets by Hawes gave Sacramento a 17-point lead with 6:34 left in the third quarter but Denver went on an 18-6 tear, slicing the deficit to 78-73 heading into the fourth. Billups, who missed 12 of his first 13 shots, connected twice from 3-point range during the flurry that was culminated by Lawson's baseline jumper with 1.1 seconds left in the third.
Denver started the fourth similar to the way it finished the third, scoring the first seven points and going ahead 80-78 on Kenyon Martin's left-handed driving layup with 10:01 remaining.
Sacramento stayed close, and Sergio Rodriguez's driving layup with 3:30 remaining pulled the Kings to 93-91. Sacramento had a chance to tie it with just over a minute remaining but Beno Udrih missed a long jumper and Billups made a driving layup to put Denver up 99-95 with 55 seconds left.
The Kings had 38 points in the second quarter, converting 62.5 percent of their shots to score the second-most points in a quarter this season by a Denver opponent, and led the Nuggets 64-50 at halftime.
Breaking away from a 26-all tie after the first quarter, Sacramento pulled in front 49-40 behind a 12-2 surge featuring two 3-pointers by Andres Nocioni. Kenyon Martin stalled the momentum with a three-point play, but the Kings outscored the Nuggets 15-8 over the next five minutes, with Jon Brockman driving in for three layups in that span to help Sacramento go in front by 16 points.
Notes: Memphis had 40 points in the first quarter against Denver on Nov. 1. ... Sacramento rookie Tyreke Evans was a late scratch because of a sore ankle. ... The Kings scored more than 100 points for the first time in seven games.
(Copyright 2010 by The Associated Press. All Rights Reserved.)