Afflalo scored 20 points, Chris Andersen had 16 points, seven rebounds and six blocks and Denver broke open a close game in the third quarter to beat the short-handed Suns 109-92.
Ty Lawson scored 17 points and rookie Kenneth Faried had 13 points and nine rebounds for the Nuggets, who snapped a five-game home losing streak.
"It was huge," Afflalo said of winning at home. "It was a great win for us in Indiana but this was even more important because we've got to start establishing ourselves on our home court to let teams know it's not going to be an easy walk here."
Nash and Hill sat out to rest and avoid risking getting hurt Phoenix coach Alvin Gentry said before the game.
"They're a little run down. I don't feel it's necessary to stick them out there with the possibility of injury," he said.
The Nuggets appreciated not having to face the NBA's assist leader.
"Phoenix kind of gave us a some slack by not playing Nash," Nuggets coach George Karl said.
Without them in the lineup the Suns struggled early but came on strong after halftime.
Denver was up 58-51 at halftime but Redd, who got the start for Hill and had 11 points at the half, led a Phoenix surge after intermission. He hit two 3-pointers and converted a three-point play to tie the game at 62-all with 8:47 left in the third.
"We played well enough to tie it up, we just couldn't keep up that pace," Redd said.
The Nuggets quickly grabbed control again with their defense and the scoring of Afflalo. Lawson had two steals, one of which led to a clear-path foul, and Kosta Koufas had two blocked shots as Denver went on a 24-8 run to end the third. Afflalo led the way on offense, scoring 13 points after it was tied, including a 3-pointer and two free throws that made it 86-70 heading into the fourth.
"We started running again," Afflalo said. "We were running the court hard, we made a few big defensive possessions -- those feed our energy."
The Nuggets held Phoenix to 33 percent shooting.
Andersen has struggled to find minutes lately but he made the most of them Tuesday. It was the third time in his career he has registered at least 15 points, five rebounds and five blocks in one game.
"That's Birdman. Definitely a wild card," Lawson said. "He was blocking everything."
The Nuggets took advantage of the absence of Nash and Hill to jump out to a 10-0 lead. Denver stretched the lead to 33-19 on Rudy Fernandez's 3-pointer late in the first.
The Nuggets quickly increased the advantage to 16 points at the start of the second quarter before Phoenix made a charge behind Redd and Morris. Morris scored 11 of his 13 first-half points in the period and Redd scored seven points -- including a 3-pointer -- in the final 1:51 of the half as the Suns pulled to within five with 19 seconds left before half.
"We missed some early shots and that didn't shake us because we were able to get back into the game," Gentry said.
Andersen has 605 blocks as a Nugget, surpassing Antonio McDyess for sixth all-time on the franchise list. ... Koufas tied a season high with three blocked shots. ... The road team is 2-14 in this series since the start of the 2007-08 season. ... The Suns are in the middle of their first of three back-to-back-to-back games this season.