After the Lakers had rallied from an eight-point deficit and grabbed a 77-75 lead late in the third quarter, Hayward scored six straight points to put Utah back in front.
After Los Angeles had trimmed a 97-90 deficit to one with less than four minutes left in the game, Hayward scored the Jazz's next six points to keep them from falling behind.
"He understands what's going on," said coach Tyrone Corbin, "and he gets us something good" in those situations.
Veteran forward Richard Jefferson believes Hayward's role as the player his teammates seek to lead them is an indication of two-way growth.
No. 1, Hayward's willingness to take the responsibility of big shots has become obvious.
"When the play breaks down and the ball's in somebody else's hands," Jefferson said, "guys look for 'G' because he's a good player. He's a very, very good player and, a lot of times, he delivers."
In the bigger picture, the trust Hayward's teammates seem to have in him has become a key ingredient to Utah's success.
"We look to him when we haven't hit a shot and it's starting to get ugly," Jefferson said. "That's not just the evolution of 'G,' but it's the evolution of the team, too."
Hayward downplayed the suggestion he was the reason the Lakers couldn't make a game-turning run in the second half.
The swingman called it a collective effort.
"As a team, we have to be able to stop runs, whether that's me or somebody else," he said. "We've gone through stretches this year when teams go on 12-0 and 14-0 runs on us, and you can't allow that.
"A timely basket by one of us executing the offense and maybe getting a layup or something stops the other team's momentum and keeps them from running the ball up the floor on us."
Hayward finished with nine assists.
"He was poised," Corbin said. "When he doesn't get shots for himself, he gets shots for other guys. He does so many different things for us."
A closer look
• Gordon Hayward finishes with 24 points as the Jazz beat the Lakers, 105-103.
• Hayward scores 17 points in the second half. He also contributes a team-high nine assists.
• Hayward scores eight of Utah's final 11 points as the Jazz hold off a late L.A. rally.