He scored 20 of his 26 points in the second half, including a go-ahead basket with 36 seconds left in regulation and seven straight points in overtime.
"They are veteran guys, and they find ways to win," said Hayward, who finished with 26 points but had only two in the final 11 minutes.
"[Pierce] has been doing that for a while. I think I can take this as a learning experience see how he controlled the game when it got to the wire and try to emulate some of that."
Jazz center Al Jefferson scored 15 points, but he took only 15 shots in 39 minutes against the Celtics' determined defense.
"It's a tough loss," he said. "It's a tough one that I feel we could have won. Pierce just made some tough shots. ... That's why they call him 'The Truth.' "
The Jazz dropped to 2-1 in overtime this season and 13-7 against Eastern Conference opponents.
Boston defeated Utah for the second time this season, despite squandering an 80-72 lead going into the fourth quarter.
"I thought our guys played hard for the most part," coach Tyrone Corbin said. "... I'm proud that we fought our way back in the game and had some chances at the end. But give them credit. They made a lot of tough shots."
After scoring 15 points, Marvin Williams said, "We were in position ... but Boston made big plays down the stretch. Those guys have been winning for a long time, so they know what to do in situations like that."