But the Nuggets turned up the defensive intensity in time, overtook the Grizzlies in the final 2:35 and defeated Memphis 111-109 on Wednesday night.
"It would have been a long plane ride home thinking about this loss," said Carmelo Anthony, who led Denver with 35 points, including the go-ahead three-point play with 33.2 remaining.
Anthony's basket completed a comeback from 17 points down in the second half. He added a pair of free throws with 5.8 seconds left for a 111-108 lead.
Memphis had one more chance, but Marc Gasol was fouled with 3.2 left. He hit the first one free throw and missed the second on purpose. Memphis was unable to corral the rebound, and Denver flung the ball into their frontcourt as the clock expired.
"This definitely was a game we let slip out of our hands," said Grizzlies forward Hakim Warrick, who finished with 16 points. "As well as we played, not coming out with a victory is tough."
"We turned it on in the fourth quarter," Billups said. "And, luckily we had time to do it."
Denver remained a half game ahead of Portland -- a 95-85 winner at Indiana on Wednesday night -- for first place in the Northwest Division.
"Every win is important to us," Nuggets coach George Karl said. "We're in a race that's got about five horses in it. We needed to get a win on the road. We haven't had one in awhile."
The Nuggets outscored Memphis 30-18 in the fourth, sending Memphis to its 14th loss in the last 16, and seventh straight against Denver.
"Defense, like it always is," Billups said about what fueled the comeback. "Just defense. Just grinding. Buckling down. Having pride."
Memphis was in early foul trouble.
With Darko Milicic sitting out because of a bad back, the Grizzlies were forced to go to the bench for the seldom-used Hamed Haddadi, the league's first Iranian player recalled earlier Wednesday from the Dakota Wizards.
The 7-feet-2 rookie responded with five early rebounds and seven points, not only a career-high in points for a game, but surpassing the five points he had scored all season.
He finished with seven points and seven rebounds.
The unexpected play from Haddadi and a dozen points from Gay, helped Memphis establish an 11-point lead in the first period.
"We've been struggling on the road," Billups said. "It was disappointing to get off to a start like that."
Part of the Memphis success was getting to the basket and outscoring the Nuggets in the paint -- a rare feat for Memphis against the Nuggets. In the previous six games between the two teams, the Nuggets had scored an average of nine more points in the paint than Memphis.
Memphis was ahead 49-38, when the foul issues mounted.
Three Grizzlies had a trio of fouls each midway through the second. Memphis held on to carry a 59-53 lead into the break behind 19 points from Gay, who hit eight of his 12 first-half shots.
Nene had scored 15 points on 5-of-7 from the floor, and finished with 19.
Memphis carried a 91-81 advantage into the fourth, but Denver's energy was picking up behind Smith's play.
"We let them get back in the game," Gay said. "If we would have executed right, and did everything and played good defense, we wouldn't be in that position."
Anthony and Billups picked up the pace in the fourth as the Nuggets began chipping away. Anthony's 3-pointer from the top of the key brought the deficit to 100-92 with 7:20 left. Another 3-pointer from Billups later, cut the lead to five.
After a 7-0 run by Denver, Anthony's wide open 3-pointer from the right of the key tied the game at 104 with 2:48 left.
Then Anthony carried the Nuggets home, scoring Denver's last 10 points.
"We're not taking nothing away from the Grizzlies," Anthony said. "Our standing is so high right now, we've got places we want to go and where we want to be.
"For us to lose a game like this on the road, would have been tough to swallow."
The Nuggets are 44-25 for the second time in franchise history, their best record through 69 games. The 1984-85 team started with that record and went to the Western Conference finals. Nuggets F Kenyon Martin, played 24 minutes. It was his second game back in the lineup after missing five of six games with a lower back strain. Nuggets reserve F/G Linas Kleiza suffered a cut to his left eye in the first half. He returned in the second half. It was Anthony's 10th game this season scoring at least 30.