A 3-point attempt at the buzzer by Denver's Randy Foye slammed off the side of the backboard to leave the Kings a winner to begin the season.
The game marked the debuts of two new NHL coaches -- Brian Shaw for the Nuggets and Mike Malone for the Kings.
Shaw replaced NBA Coach of the Year George Karl after the Nuggets' early exit from the playoffs last year.
Denver also started just one player from last season's opening lineup and that one -- Ty Lawson -- has been bothered by a groin injury.
The game was close throughout the fourth quarter and Thompson's game-winning dunk accounted for his only two points of the contest.
DeMarcus Cousins led the Kings with 30 points and 14 rebounds while Greivis Vasquez had 17 points.
Denver was paced by 20 points from Lawson.