Hayward scored 23 points, including the winning basket with 4.5 seconds left, and the Jazz rallied for a 104-102 victory over the Sacramento Kings.
Williams added 20 points, including going 7-for-7 from the line -- part of a huge disparity that played a key role in Utah's rally. The Jazz trailed by 13 with 8 1/2 minutes left.
"I thought we won with a lot of grit, gut, staying together," Corbin said.
Utah's big rally was even more impressive considering starting point guard Mo Williams sprained his right ankle in the first half and was in a walking boot after the game.
The Jazz stepped up their defense, got aggressive at the other end and made the most out of their opportunities at the line.
"We got stops, we rebounded and we attacked," said Al Jefferson, who finished with 19 points and eight rebounds.
The Kings had one final shot but James Johnson's running jumper at the buzzer bounced harmlessly off the rim, and the Jazz (7-6) remained perfect at home.
"It says a lot that we were down by a lot, knowing that we didn't hold our heads down," said Jamaal Tinsley, who teamed with reserve Earl Watson to pick up the slack when Mo Williams went out midway through the second quarter.
Tinsley missed his final shot after Thornton had tied it at 102 with a 3-pointer with 55 seconds remaining. But Tinsley stole the ball back from point guard Aaron Brooks with 15 seconds to go, setting the stage for Hayward's big shot.
Tinsley, 34, prides himself on playing good defense.
"The last nine minutes, we just came out and gave it our all," said Tinsley, who had 12 assists, six rebounds and two steals.
The Kings were left shaking their heads, wondering what went wrong.
"I don't know," Evans said. "No way we should have lost that game (after) being up by a big margin."
The Kings led 92-79 with 8 1/2 minutes left but couldn't hold on. Hayward, Marvin Williams, Derrick Favors, Tinsley, Jefferson and DeMarre Carroll each played a key role in Utah's comeback. Favors finished with 16 points, 14 rebounds and a pair of blocked shots.
Carroll's fast-break layup ignited the crowd, and Jefferson had a key steal against DeMarcus Cousins with the Jazz down just three.
Jefferson's putback gave Utah a 102-99 lead but Thornton tied it with a 3-pointer, only to have Tinsley make the key defensive play against Brooks and set Hayward up for the winner.
"We turned the ball over, unfinished plays, everything we had done to get in that position on the road, in this building against a good team where you don't win that often," Kings coach Keith Smart said. "Too much one-on-one, and it cost us the game."
The rally spoiled another homecoming for former Brigham Young star Jimmer Fredette, who was making his third professional visit to Utah. Fredette hit three 3-pointers and finished with 10 points, enduring a mix of cheers and boos.
While he earned more playing time Friday than he had seen in the previous three games combined, the loss was what mattered.
"It just crumbled for us," Fredette said.
Corbin was most proud of the defense.
"You get some stops and you feed off them," he said. "You get plays that make your team feel the momentum change. One leads to another, and you close down a little bit. The guys just feed off each other."
The teams turn around and play Saturday in Sacramento. ... Watson was active for the first time since tearing cartilage in his right knee April 8, then undergoing season-ending surgery later that month. He finished with two assists and two rebounds, and had a crowd-pleasing alley-oop pass to Hayward in the fourth. ... Cousins started slowly and finished with 14 points for the Kings, but he also had four turnovers and made key fouls late on Utah's guards.