Noah was listed on the starting lineup sheets handed out a few minutes before the game. But he told Miller in the locker room that he was going to sit out because of a left foot injury. Miller responded with a season-high point total, going 9 for 14 from the field.
"How many layups did I make? That helps your shooting percentage," Miller said after making his 10th start of the season. "You get those easy ones, and then the game flows and you just kind of get that confidence."
Noah was hoping to return Monday night in San Antonio.
"I just couldn't get going," Noah said. "I got a massage earlier, I just tried everything I could. The pain is just too much right now. I'm just happy we won the game. Brad played huge."
The 7-foot Miller sank two 3-pointers, went 5 for 5 from the free-throw line and grabbed a key offensive rebound in the final minute. He played three seasons in Sacramento for Houston coach Rick Adelman and said his familiarity with the Rockets' system helped him have a big game.
"I liked that staff, I've always been friendly," Miller said. "Must've brought a spark from the old days. I know how they're going to do every aspect of offense and defense. I always like to play well against them."
Derrick Rose scored 20 points, and Kirk Hinrich added 12 points and seven assists for the Bulls, who've won six of their last eight games.
Chicago led from start to finish, shooting 53 percent (39 of 73), going 7 for 12 from 3-point range and outrebounding Houston 42-32.
The Bulls improved to 3-7 in the second game of back-to-back sets. They won in Phoenix on Friday night and didn't arrive at their hotel in Houston until about 4 a.m. Saturday.
"That's the NBA," Miller said. "You're going to be tested at some point, and you can use it as an excuse. We just went out and competed tonight."
The Rockets, meanwhile, lost for the first time in five home games that were the second half of back-to-back sets this season. Houston shot 55 percent in a win in San Antonio on Friday night, but only 40 percent in Saturday's loss.
"We just came out and thought we had all day to get in the game," Adelman said. "I don't know if it is that we beat San Antonio and we thought this was going to be a cakewalk. We talked about that this team is very good offensively. We really buried ourselves in the first half."
The Bulls showed no signs of fatigue after their long night, shooting 63 percent in the first half to build a 12-point lead. The Rockets opened the third quarter with an 8-0 run, after the Bulls missed their first five shots after the break.
Houston trailed only 80-75 after three quarters, and cut the deficit to two before Miller sank two 3-pointers to start a 9-0 Chicago run. Miller assisted on Gibson's dunk with 5:23 left to put Chicago up 97-86.
The Rockets rallied one more time, cutting the deficit to two on Landry's three-point play with 1:56 left and Brooks' 3-pointer 20 seconds later. Gibson missed two free throws with 48.9 seconds to go, but Miller grabbed the rebound on the second one and Rose swished a pullup jumper with 30 seconds remaining to make it 101-97.
Gibson blocked Brooks on a drive at the other end, and the Bulls won in Houston for only the third time in the last 14 trips.
The 6-foot-11 Noah had started all of Chicago's first 41 games. He scored 19 points in 25 minutes Friday in a win in Phoenix. ... The Rockets faced a double-digit deficit for the fourth straight game. ... Gibson has five double-doubles this season. ... The Rockets finished with 18 assists, snapping a streak of 11 consecutive games with at least 20.