Hinrich scored 11 of his 19 points in the first quarter as the Bulls built an 11-point lead before beating the Utah Jazz 103-98 on Saturday night.
"I was finding myself open, I was able to get some 3s to go in early and I guess that kind of jump-started us," said Hinrich who made 3-of-4 3-pointers in the first period. "On the other hand we were playing real good defense, and offensively we are playing real well together."
Mehmet Okur had a career-high 33 points and 17 rebounds for Utah, which played most of the game without Andrei Kirilenko after he injured his left ankle early in the second quarter.
The Bulls led 32-21 after shooting 67 percent in the first quarter, making eight of their last nine shots. Gordon's jumper with 9:41 left in the second capped Chicago's 25-6 run that gave it a 40-24 lead.
The Bulls' reserves scored 52 points and shot 20-of-30 from the field.
"The bench was very good," Chicago coach Scott Skiles said. "I thought Luol Deng, in particular, stood out."
Bulls guard Chris Duhon, who missed Wednesday's game against Golden State with a right knee contusion, started and scored 12 points.
Kirilenko left the game early in the second quarter after he sprained his left ankle. He landed on Chicago forward Othella Harrington's foot after attempting a 3-pointer. Kirilenko was helped to the locker room and did not return to the Jazz bench. He will be re-evaluated on Sunday.
"We'll do some treatments. I think I'll be all right in about a week," Kirilenko said.
Kirilenko missed 41 games last season -- 26 after spraining his right knee on Nov. 30 and then 14 more with a wrist injury.
Jazz rookie Deron Williams, who led Illinois to the highest win total in school history and championship game of the NCAA Tournament earlier this year, received a nice applause when he checked in to start the second quarter. He finished with 13 points.
"It was great to come back here," Williams said. "It would have been much better with a win. I think this is my first loss here [United Center]. The story of the night we could never get over the hump."
Williams' jumper cut the Chicago lead to 72-69 late in third quarter and the Jazz got within 87-85 on a pair of free throws by Milt Palacio.
The Bulls came back with a basket by Deng, and Hinrich followed with a three-point play.
Okur tried to keep the Jazz in it with a long jumper with 1:56 left, cutting Chicago's lead to 96-93, but Hinrich followed with two free throws and Deng had a dunk to stretch the Bulls' lead to seven points.
"We did a great job of hanging in there," Deng said. "We knew they'd make a run. I wish we could have held them off better and kept our mental edge, but we got through it."
Palacio scored all eight of his points in the fourth quarter and Gordan Giricek added 14 for the Jazz.
Williams' former coach at Illinois, Bruce Weber, presented the game ball before tipoff. ... Tyson Chandler had 11 rebounds for Chicago. ... Chicago's reserves have outscored their counterparts in every game this season.