It also moved them closer to securing a postseason spot of their own.
Denver seeks its fifth win in six games Wednesday night at the Pepsi Center, but Los Angeles will be looking for a fifth consecutive victory and a third in four tries against the Nuggets this season.
Thanks to the Nuggets' 105-102 victory at Houston on Monday, the Clippers (38-23) had locked up their first playoff berth since 2006 before defeating Oklahoma City 92-77 later in the night.
Blake Griffin scored 17 points and grabbed 11 rebounds for Los Angeles, which has loftier goals than simply qualifying for the postseason.
"It is something that we're happy about, but by no means is that all we want," Griffin said. "That was one of our goals coming in, but it goes farther than that."
Chris Paul, acquired from New Orleans in December to help turn around a franchise that has won a single playoff series since 1976, scored 12 points and added 10 assists.
The surging Clippers have won 12 of their last 14.
"This is a great feeling," Paul said. "We can celebrate it, be excited about it tonight but tomorrow we're back at work."
Los Angeles' lone playoff series victory in the last 35 years came in five games over Denver in 2006 - also the last season the Clippers took three regular-season meetings from the Nuggets.
Paul had 25 points and seven assists in a 109-105 road win Jan. 29 in the first matchup. Danilo Gallinari scored a game-high 21 points in Denver's 112-91 victory Feb. 2, but Paul's season-high 36 helped the Clippers to a 103-95 win Feb. 22 in the most recent meeting.
The stakes are higher this time around, with the Clippers chasing the Lakers for the Pacific Division title and the Nuggets (34-27) trying to secure their own postseason spot.
With Monday's win, Denver moved into sixth place in the Western Conference, one-half game ahead of defending champion Dallas and two games clear of the Rockets and Phoenix.
"Our awareness of where we are in the season is really starting to heighten now," Afflalo said. "Before, we used to go out there and compete and play the games. Now, we have an ulterior motive almost, in terms of understanding playoff positioning. That's good for a young team."
Coach George Karl's squad has won a season-high five straight at home. This will be his 20th consecutive season as an NBA coach with a team finishing .500 or better.
"We had opportunities to give up on the game and we didn't do it," Karl said. "It's a huge win for us."
The Nuggets have averaged 107.8 points over their last five games, and they lead the league with 103.6 per game this season. The Clippers, though, held the high-powered Thunder to a season-low 25 points in the second half Monday, keeping their opponent under 100 for the 13th time in their last 15 games.
"We have enough offensive power to play with anybody, but our defense is what triggers us," Paul said.
The Clippers' road win over the Nuggets in January ended a nine-game skid in Denver.