"We have to play hard to win games," Gasol said. "We are not that good to just come out and be casual, make a shot, don't run back and don't rebound because we are not that good."
The Nuggets closed the game on a 9-0 run, with Gallinari scoring six points in the final two minutes, including the 3-pointer, which was set up when he intercepted a pass by Gay on the Grizzlies' end of the floor.
Gallinari connected on five of his first six shots and all four of his free throws in the first half to help the Nuggets carry a 52-49 lead into the break.
Gay led Memphis with 11 points at the half.
Neither team led by more than five in the opening two quarters, with eight lead changes and nine ties. There ended up being 12 ties and 12 lead changes in a tight game.
Memphis opened the second half with a 12-4 run, but McGee had eight points in the frame to cut the Grizzlies' advantage to 70-69 entering the fourth.
Denver would carry its rally into the final frame with eight straight points, including six by Faried. The two teams would continue exchanging leads throughout the fourth, and were still tied at 87 with 3:35 left.
Memphis took a 92-88 lead on Randolph's tip-in with 2:14 left, but the Grizzlies didn't score again.
It was a nice recovery for the Nuggets, who were coming off a poor showing in a 126-100 loss at San Antonio on Thursday night.
"We played our worst game of the year in San Antonio," Karl said. "Our guys, most of the time, have showed a big heart. .This was the first game on the road where I think we executed at a high level both offensively and defensively."
As for the impact of Gallinari's 3-pointer, Lawson added: "We've had a rough 10 games. For that shot to go in was big for us, for our morale. To get a big one like this is huge."
NOTES: The Grizzlies ended up matching the franchise-best eight-game winning streak from January 2004. ... The loss also snapped Memphis' 15-game regular-season winning streak at home. ... Denver had lost three straight to the Grizzlies, all last year by a total of seven points. ... Denver has outrebounded its opponents in nine of the last 10 games. ... The NBA announced before the game that Randolph was fined $25,000 for his confrontation with Kendrick Perkins after both were ejected from a game in Oklahoma City last week. .Faried's 13points and 13 rebounds marked his seventh double-double of the season. ..Randolph has double-doubles in all 10 of Memphis' games this season.