The Jazz got off to a fast start behind two of their new additions, with Mo Williams scoring 10 first-quarter points and Marvin Williams adding eight as Utah took command early.
The Jazz were without Millsap and backup point guard Jamaal Tinsley, both excused for personal reasons.
The Thunder did not play Sixth Man Award winner James Harden because of a groin injury, and remain without Kendrick Perkins (wrist surgery) and Thabo Sefolosha (bruised quad).
Brooks had specific goals early, and one of them was on the boards. He was pleased that his team limited the Jazz to four offensive rebounds in the first half.
But he was hoping to see some solid play from his backup point guards.
Reggie Jackson got the start and finished with 10 points, but made just 3 of 10 shots and had seven turnovers.
"I'm disappointed with my performance," Jackson said. "I was trying to make too many home-run plays instead of just making plays."
Eric Maynor played 12 minutes and had four points on 2 of 8 shooting.
Serge Ibaka, in his first game since the Olympics, finished with 12 points and seven rebounds for Oklahoma City. He missed the preseason opener because of a bruised quad.
Cole Aldrich added 11 points, 10 rebounds and three blocks for the Thunder but had several of his own shots swatted by Favors.
Favors finished with three blocks but didn't get the call on a few others, including a hustle play when Jackson appeared headed for a fast-break layup after a Jazz turnover.
He said he felt "cheated" out of a few blocks, but wasn't worried about shooting 0 of 5 and finishing with 1 point.
"I'm a defensive player; the shots will fall," Favors said.
NOTES: Jazz rookie Kevin Murphy made his preseason debut with 3:11 left in the second quarter and finished with two points. ... Asked about Jazz 6-11 backup center Kanter dropping 51 pounds to 242 this offseason, Thunder coach Scott Brooks quipped, "He's a small forward now." ... Oklahoma City dropped to 0-2 in preseason after going undefeated during the NBA's abbreviated 2011 preseason schedule. ... The Thunder made just 3 of 15 shots from 3-point range and 29 of 78 overall.