Rose scored 18 points, including eight during a furious fourth quarter rally, to help the Bulls beat the Denver Nuggets 94-92 on Monday night.
"Derrick struggled a lot," said Bulls forward Luol Deng, who added 17 points. "That's going to happen because we play so many games. It was just a good team win."
Taj Gibson had 16 points for the Bulls.
Denver led 80-74 with just under seven minutes left before Chicago went on a 16-6 run sparked by Rose.
Carmelo Anthony's basket with 15.3 seconds left cut the Bulls' lead to 90-88. Joakim Noah hit a free throw to extend the margin back to three points. Deng fouled Anthony, who made two free throws, to make it a one-point game with 11 seconds left.
"They got the last run," said Anthony. "We made our run in the third quarter."
"Chauncey just made a great play," Afflalo said. "He made a great play. I'm trying to take the blame for missing that shot little bit. Actually I thought he was shooting. He was leaning, but he made a smart basketball play.
"I took an off-balance shot and I couldn't square up like I wanted to, otherwise I think I would have made it."
Chicago hit two more free throws and Afflalo missed a 3-pointer that would have tied it.
Anthony led Denver with 32 points.
Noah had 13 points and 19 rebounds for Chicago. He's now had a double-double in all six of the Bulls' games, the franchise's first player to do that since Artis Gilmore did it in the first 11 games of the 1978-79 season. Noah leads the NBA in double-doubles.
"[Noah] blocks shots and holds the paint down," said Anthony. "[He is an] energy guy who got 19 rebounds, you can't ask more than that for a big guy."
Rose's big fourth quarter helped offset a shaky first three. Rose was 3 for 16 from the field after three quarters, but 4 for 5 in the final period.
"Derrick is our leader," Noah said. "His shot wasn't falling but down the stretch, he put the game on his shoulders. That's why he's such a special player."
The Nuggets got back center Nene, who missed three games with a groin injury. He got off to a quick start scoring eight points and grabbing five rebounds in the first quarter as Denver built a 28-23 lead.
The Bulls responded in the second quarter outscoring Denver 27-15 to take a seven-point halftime lead.
"I liked our fight," said Bulls coach Tom Thibodeau. "We started off a little slow [in the second quarter], we came back and got aggressive."
Chicago extended its lead to 10 in the third quarter before Anthony took over.
He scored 10 of the Nuggets 12 points during a 12-0 run to close the period. He started the spurt with a putback and then converted a three-point play. He followed that with a 3-pointer before finishing the period with a 20-footer.
Denver led by as many as six points in the fourth quarter, but the Bulls mounted a run midway through the final period, capped by Rose's driving layup that cut the lead to 80-78. That forced Denver coach George Karl to call a timeout with 6:26 to play in the game.
"Chicago played with a passion to win the game and I thought we matched it," said Karl.
Nene played in just three of the Nuggets' first six games, averaging 10.3 points. ... Carlos Boozer missed Monday's game for the Bulls. He's been out the entire season with a broken bone in his right hand. ... Chris Andersen (right knee patella tendon) and Kenyon Martin (left knee patella tendon) both sat out. Neither player has appeared in a game yet this season.