The Jazz snapped a six-game losing streak and improved their record to 2-14 by beating the Bulls for the first time in four seasons.
"It wasn't the prettiest win," said Burke, "... but it was a good one."
The victory was a welcome relief for Utah.
If they hadn't finished it, the Jazz would also be shaking their heads, wondering when they would get their second win, given how this game set up perfectly for them.
Chicago was playing back-to-back and its fourth game in five nights.
The Bulls were also coming to terms with the emotionally devastating news that All-Star point guard Derrick Rose underwent season-ending knee surgery earlier in the day. He also missed last season because of a knee injury.
The situation couldn't have been more deflating for the Bulls, who many predicted would contend in the Eastern Conference because of Rose's return.
Before playing the Jazz, however, coach Tom Thibodeau was resolute that his team would not stop fighting.
"The mindset is good, the character of our team is good [and] we're looking forward to the challenge," he said.
Bravely, Thibodeau predicted Rose would return from another serious injury to once again lead Chicago: "He has great mental toughness. He'll be fine. This is a bump in the road. We expect him to make a full recovery."
The Bulls were certainly competitive against the Jazz, even under the most adverse conditions.
Utah owned a 12-point lead late in the third quarter, but Chicago fought back.
The Jazz misfired on 13 of 15 possessions in one stretch and almost inexplicably found themselves trailing with less than a minute left when Luol Deng's two free throws gave the Bulls a 77-75 lead.
Richard Jefferson kept Utah alive, however, with a three-point play that made it 78-77. Joakim Noah tied the game with a free throw with 32.2 seconds remaining.
Both teams failed to win on their final possessions in regulation the Jazz on Hayward's missed jumper and Chicago on Deng's miss and Carlos Boozer's failed follow at the buzzer.
In overtime, Burke's 3-point shot gave Utah an 83-78 lead with 3:10 remaining. Coming off a pick-and-roll, he abruptly pulled up and fired over the Bulls' Taj Gibson.
"I'm starting to get my confidence back," Burke said.
Moments later, Jeremy Evans turned Hayward's lob pass on another pick-and-roll into a thunderous slam that finally put Utah in control, 85-78.
Still, even the Jazz felt a little sorry for Rose and the Bulls, who slipped to 6-7 only 13 games into what had been a season of great expectations.
"Sad for the guy," said coach Tyrone Corbin. "I know how tough it was for him last year, to miss the entire season. He worked his tail off to get back and it seemed like he was turning a corner feeling better about himself. To get another injury is just an unfortunate part of the business."
Said Williams: "Obviously everyone in this locker room sends out prayers to [Rose]."
Storylines Beating Chicago
R The Jazz earned their second win of the season with an 89-83 overtime victory over Chicago.
• Rookie Trey Burke's three-pointer in overtime helps Utah improve its record to 2-14.