The illness and injuries only seemed to be a rallying force, however, as they cruised to a 103-88 victory to stay within a game of the eighth-place Los Angeles Lakers in the Western Conference playoff battle.
"To be honest, the game was for the playoffs, but when (Kanter) went down I had to step up even more," said Jefferson, still nursing a busted lip from a shot to the mouth in Monday's win. "We're going to fight for him to the end, make his injury worth something."
Jefferson wasn't the only one, though he finished 12 of 23 with nine rebounds, two blocks and two steals.
Derrick Favors grabbed 13 rebounds in 24 minutes for the Jazz, who held a 46-36 edge on the boards.
The Suns had pulled within 75-71 going into the fourth thanks to Wesley Johnson's 10-point third quarter, including a 3-pointer at the buzzer.
Utah held the Suns to 17 points in the fourth on 35 percent shooting, while outrebounding Phoenix 17-7 to close out the game.
Johnson had a season-high 22 points and Luis Scola 20 to lead the Suns, who dropped their fourth straight.
With Phoenix out of the playoff picture, the Suns chose to rest leading scorer Goran Dragic, who was coming off a season-high 31-point, 12-assist effort in a 102-100 loss to Brooklyn on Sunday.
While the Suns left with another loss, Kanter departed the arena with a huge smile on his face despite the sling on his shoulder.
"Oh, I'll come back this year," Kanter vowed. "Yeah, I'll come back."
The injury was enough to make teammates cringe as they watched the 6-foot-11, 248-pound Kanter leave the court in obvious pain with 10:23 left in the second quarter after Suns' 7-2, 265-pound center Hamed Haddadi fell on him as they battled over a loose ball.
Kanter was biting hard into his mouthpiece, supporting his left arm and stopped courtside, thinking about trying to pop the joint back into place. Team trainer Gary Briggs led him to the locker room shortly thereafter.
"I tried, but I couldn't' do it," Kanter said.
It was enough for Randy Foye to feel sick to his stomach. Then again, he already was from an illness that kept him up all night and in the bathroom, and unable to go through Wednesday's short morning workout.
"It was pretty gross," Foye said of Kanter's injury. "But he's a tough kid. I hope he has a speedy recovery."
Jefferson, who had 27 points combined the previous two games, said he's seen similar injuries that have kept players out two to four weeks. The Jazz have 10 games remaining over the next three weeks.
Kanter is averaging 7.3 points and 4.4 rebounds for Utah while playing with the second unit, but led the Jazz in scoring in Dallas last week with 17 points.
"Guys are beat up," said Jazz forward Marvin Williams, who played through right heel bursitis "Paul (Millsap) is a little sick, Randy's been sick, my heel's a little beat up, but ... we'll fight through it."
It helped that they didn't have to face Dragic.
"We're just kind of shutting him down," Suns interim coach Lindsey Hunter said before the game. "He's been playing a whole lot of minutes and we're going to give him a break periodically through these last couple of games. If you watched him come out of games, he's looked like he's been in a brawl."
The Suns have long been out of the playoff race, but they do have a vested interest in seeing the Jazz finish ahead of the Lakers for the eighth seed. If the Lakers miss the playoffs, the Suns get the Lakers' draft pick that is not lottery protected as part of the Steve Nash deal.
Utah opened the fourth just as it started the game, with hot shooting and a take-it-to-them attitude.
Jefferson scored on a layup, converted a three-point play and hit a midrange jumper and Alec Burks added a 3-pointer as the Jazz stretched their lead to 85-71 with 8:58 left.
"Little plays are what win you basketball games," said Williams, who kept a rebound alive during Utah's 19-5 fourth-quarter run. "When you can sneak in there and get another offensive possession or maybe dive on the ground for loose ball, those are things that will put you over the top."
The Jazz on Wednesday signed former Marquette standout Jerel McNeal to a 10-day contract from the D-League's Bakersfield Jam. The 6-3 guard finished his college career as Marquette's all-time leader in scoring, steals and games played, but went undrafted in 2009. ... Former Jazz C Mehmet Okur attended Wednesday's game. ... Marshall made his first career start and opened 0 for 3 with a pair of first-half turnovers, but had nine assists in the first half. He finished with seven points and 13 assists. ... The Jazz scored a season-high 34 points in the first quarter.