The fourth-year swingman scored 12 of his season-high 30 points in the fourth quarter, helping the Jazz (6-19) to their second straight road win.
The soft-spoken Hayward has been tasked with leading the Jazz and has drawn more attention from other teams than ever before.
"It's weird when there's not anybody on you," he said before the game. "It's different. It's different this year."
But it's a role Hayward said is definitely within him.
"It is. It definitely is," said Hayward, who also grabbed a career-high 13 rebounds to go along with five assists. "I'm growing as a basketball player and learning. [If] we don't have some of those close games that we lost early this season, we probably don't close this one out."
Coming off their best offensive performance of the season, a 21-point win in Sacramento, Calif., two nights earlier, the Jazz continued their hot shooting in the first quarter at Pepsi Center.
Marvin Williams started the trend, knocking down a 3-pointer just 30 seconds into Friday night's game against the Nuggets. Richard Jefferson hit two of his own. Then Hayward and Trey Burke got into the action.
The Jazz hit 10 of their first 14 shots, including 6 of 7 from 3.
And while their shooting cooled in the second, Denver's struggles were worse. The Nuggets, playing their first game at home after a six-game trip, shot just 28 percent from the floor and scored only 16 points in the second, allowing the Jazz to take a 53-44 lead into the locker room at the break.
The Jazz went on to build up a 16-point lead in the third before things started to unravel. The Denver bench, led by Jordan Hamilton and Timofey Mozgov, soon erased the Utah advantage.
"This team's explosive," Jazz coach Ty Corbin said of the 13-9 Nuggets. "They can score a lot of points in a short amount of time and they did that in the third quarter."
The Nuggets would lead by as much as four in the final period.
Then Hayward and Derrick Favors went to work.
Hayward finished at the rim while drawing a foul and later hit a tough fade-away basket, all part of an 11-of-18 shooting night.
Favors, meanwhile, put his head into the chest of Mozgov, scoring before falling to the ground.
"I thought I broke my neck on that play," he said afterward with a smile. "That's why I was laying on the ground 'cause I hit my neck. I asked [Hayward] did it go in. I didn't even know I made the basket."
Favors' free throw pushed the Jazz lead to six and he made sure the Nugget wouldn't get closer forcing Mozgov into a tough shot on the next play and later swatting Denver's Wilson Chandler, who tied Hamilton for a team-high 17 points.
Favors' 19 points made him one of six Jazz players in double digits.
"They're growing into the roles that we're looking for them to play for this franchise," Corbin said of Hayward and Favors, his young co-captains. "Although it's new to them, they're growing every night. They're learning what it's going to take to be that next level player on a consistent basis."