"You always bring it against the best," the Jazz swingman said after the game.
Hayward answered Durant's free throws with a 3-pointer, and then another. He earned a trip to the foul line himself, then nailed a long 2.
In the end, the Jazz's young co-captain scored his team's final 17 points, holding off the surging Thunder 112-101 Tuesday night.
"I was in the zone a little bit tonight," Hayward said after finishing with a career-high 37 points to go along with 11 rebounds and seven assists.
It was a good place to be for Hayward, who has struggled with his shot at times this year. With the Jazz finally at home for an extended stretch, Hayward said he has been able to log extra hours in the gym at nights and has worked on his jump shot avoiding falling away from the basket after watching film with the team's assistant coaches.
"How 'bout Gordon tonight?" Jazz coach Ty Corbin said. "He was huge. We needed every last basket that he made for us."
Corbin praised Hayward's all-around performance.
"Not only on the offensive end, but defensively I thought he made some plays for us," the coach said. "He got his hands on some balls. He carried us down the stretch just by making plays. They really worked him tonight and he got what he wanted. He was determined to get the ball where he wanted."
The Jazz got off to a hot start in the game, hitting 12 of their 17 shots in the first quarter. Behind solid play from Enes Kanter and the reappearance of guard Brandon Rush, who hadn't scored a basket since mid-December, the Jazz held a 21-6 bench scoring advantage at the half.
Utah pushed the lead to as much as 24, as all five Jazz starters reached double-figures in scoring.
Big man Derrick Favors had 15 points and five rebounds. Forwards Richard Jefferson and Marvin Williams had 10 and 12 points, respectively. And rookie point guard Trey Burke added 10 points, six assists and six rebounds.
The Thunder were missing point guard Russell Westbrook, who is out possibly until after the All-Star break, and Ibaka, who was dealing with flu-like symptoms.
Their absences left Durant with little help.
Point guard Reggie Jackson had 20 points, but no other Thunder player reached double-digits.
But that didn't stop Durant from making a push.
"They have the second-best player in the world on their team and he got going," Jefferson said.
But Tuesday night would belong to Hayward and the Jazz, who improved to 12-25 on the year.
"I don't think earlier in the season we would have been able to do that," Hayward said. "We're growing as a team. It's good to see we can withstand somebody's run and make one of our own."