Billups, though, hasn't been able to help his hometown team end a losing streak against one of his former clubs.
While searching for a third straight win, Denver will also try to beat the visiting Detroit Pistons for the first time in nearly four years Friday night.
The Nuggets (38-19) originally got Billups - a Denver native and former Colorado star - in 1999 after swinging a trade with Toronto. After stints with Orlando, Minnesota and Detroit, Billups was sent back to Denver from Detroit in November 2008 as part of a four-player deal involving Allen Iverson.
Since then, only the Los Angeles Lakers (105-32) have a better record among West teams than the Nuggets (91-45). That success, however, has not translated against the Pistons, who are 57-79 in that same span.
Denver suffered its seventh straight loss to Detroit 101-99 on Dec. 10 as Billups missed a layup in the final seconds.
"I got what I wanted," he said. "But I tried to get the foul too much."
Carmelo Anthony had 40 points and Billups finished with 21, but the Nuggets couldn't rally from a seven-point deficit entering the fourth quarter and lost for the 22nd time in 26 meetings with the Pistons.
Since that game, the teams' performances couldn't be much different. The Pistons (21-36) have gone 11-24, including Wednesday's 97-91 loss at the Los Angeles Clippers.
In the second of a four-game trip, Hamilton gave his team a one-point lead on a 3-pointer with 44 seconds left remaining in its bid for a third straight win. Detroit, however, failed to score after that.
Hamilton, who had made 51 straight free throws entering the game, also missed on three consecutive attempts with eight seconds left. Despite going 2 of 8 from the line, he finished with a team-best 21 points, his sixth straight game with more than 20.
"It shouldn't have come down to that, but that's what happened," said Prince, who chipped in with 17 points and 10 rebounds. "That's why you've got to play good for 48 minutes and not let the other team hang around long enough to make big shots and big plays at the end of the game.
"We stopped our flow, and that was it."
The Nuggets, meanwhile, have gone 22-12 since losing to the Pistons - highlighted by a season-high eight-game winning streak from Jan. 11-27. However, they alternated wins and losses in their previous seven games before Thursday's 127-112 victory at Golden State.
Billups led the way with 37 points and hit six of Denver's season-high 16 3-pointers. Anthony added 27 points, and J.R. Smith had a team-leading seven 3s and finished with 25 points.
The Nuggets played their first game without coach George Karl, who revealed on Feb. 16 that he has neck and throat cancer. Former Piston Adrian Dantley led the team in his absence.
"George told us just to focus on the game and not worry about him," Dantley said. "The main thing with George is he wanted the win. We got that. It was weird, but I'm glad this game is over."
Karl is expected to return Friday.
The Nuggets haven't beaten Detroit since a 98-87 home victory on March 1, 2006, and have dropped three in a row at home to the Pistons.