Jefferson has often struggled against the Australian center, but took advantage of Bogut's absence with 26 points and 10 rebounds in the Jazz's 85-73 victory over the Bucks.
"I looked at it like I had a good opportunity to get going. I wanted to be more active," Jefferson said.
After shooting 2 for 16 in the season opener, Jefferson has steadily improved to again take his place as the centerpiece of Utah's offense.
"I've been a scorer all my life. That's why I didn't panic after that first game," he said. "My teammates have kept their trust in me and kept getting the ball into me."
Paul Millsap had 13 points and 12 rebounds and Gordon Hayward added 12 points for the Jazz. Hayward scored five points on back-to-back possessions and Millsap added a jumper on the next offensive set to clinch the game with 1:07 to play.
"They gambled a little bit and overextended themselves and I was able to take advantage of it," Hayward said.
Drew Gooden had 24 points and 12 rebounds for the Bucks but didn't have the inside presence of Bogut as the Jazz had plenty of point-blank looks at the basket. Bogut missed the game due to personal matters and Mike Dunleavy was out with groin pain.
"It's tough," Gooden said. "We can't win scoring 70-80 points."
The Bucks also won't win many games unless they shoot better. Led by Brandon Jennings' 4-for-19 performance, the Bucks were just 31 percent and had 10 shots blocked by the Jazz, including a career-best five by Derrick Favors.
"Derrick was superman out there with his five blocks. He did a great job converging on shots inside," Utah coach Ty Corbin said.
The game marked the third back-to-back set of the compressed season for the Jazz. They lost the back end of the other two, but were playing at home on consecutive nights for the first time since 2008 and improved to 3-0 in Energy Solutions Arena.
"When we bring the energy and the crowd gets behind us, it's just kind of a snowball effect and we're able to create a run," Hayward said.
The Jazz experienced injury problems of their own with Josh Howard and Devin Harris. With 1:53 left in the first quarter, Howard went to the locker room with a left quad strain and did not return. Harris left the game with 6:37 left in the third period with a strained left calf and also missed the rest of the contest.
Millsap limped off the court midway through the fourth quarter but returned to help the Jazz close out the Bucks. The injuries forced the Jazz to play rookie Alec Burks a season-high 28 minutes and showed some odd combinations Corbin hadn't played before.
"With our team, we're going to have to use everybody and Burks maximized his time," Corbin said after Burks finished with nine points and six assists.
The Bucks couldn't hit open jumpers and had little luck driving into the paint. Stephen Jackson was the only other Milwaukee player in double figures with 16 points but shot 5 for 17.
"It was a big deal for us to get stops. We know we can score, but we need to stop people," Favors said.
The Jazz, who lead the league in blocked shots, took advantage of Bogut's absence early to get 30 points in the paint in the first half and block nine Bucks shots on their way to a 43-34 halftime edge. Poor free-throw shooting and 14 first-half turnovers were all that kept the Bucks within striking distance.
Utah finished with 24 turnovers, but was in front since midway through the first quarter.
Though Jefferson was relieved not to oppose him in this game, he wished Bogut the best in whatever personal matters he's facing. ... Former Milwaukee coach and current University of Utah coach Larry Krystkowiak was in attendance. ... Milwaukee's last win in Salt Lake City was October 30, 2001, when Ray Allen had 32 points. ... The Bucks set a season low in a half with just 34 points in the first two periods and Milwaukee finished 2 for 21 from beyond the arc.