In a battle that raged from start to finish, home team Memphis led 92-88 with about two minutes remaining but failed to close the game out, going scoreless and making critical mistakes in the final moments.
"We got what we deserved," the Grizzlies' Marc Gasol said. "The last game we didn't play that well, but the other team wasn't as talented as (Denver). When you play with fire, sometimes you get burned."
Momentum switched back and forth the whole game as the Grizzlies went up by five in the third quarter on the back of a 14-4 run, before Denver returned the favour with an 8-0 stretch that put them ahead 77-70 early in the fourth.
The Nuggets out-rebounded Memphis 47-33, with Kenneth Faried grabbing 13 to go with his 13 points.
Nuggets forward Danilo Gallinari made three free throws and, after JaVale McGee put visiting Denver on top 93-92, he drained a three-pointer in the last seconds to seal the win.
Gallinari finished with a game-high 26 points, McGee added 15 and eight rebounds off the bench as the Nuggets (5-6) brought a run of three straight defeats to an end.
"This is the first game on the road where I think we executed at a high level," said Denver coach George Karl. "We've got to get better at making shots and I think we will once we win games, and I think confidence comes by winning."
After losing their season opener, Memphis (8-2) had run through their competition until facing Denver.
Rudy Gay led the way for the Grizzles with 22 points, while Zach Randolph put up 12 points and 13 rebounds.
Memphis coughed up two straight turnovers in the final minute, and kept putting Denver on the foul line as the game slipped away.
Despite the loss, the Grizzlies stayed a half-game ahead of San Antonio for the Southwest Division lead after the Spurs lost to the Los Angeles Clippers.