TYLER Herro should still be in college. He’s not, but is still a student..

He carries a red spiral-bound notebook with him at all times, jotting down notes when things pop into his head. What worked, what didn’t, where he thinks he can get better and how he’s feeling after a game.

“It helps me get locked in, helps me focus,” Herro said.

Whatever he read Wednesday night helped him put together the game of his life – and carry Miami Heat a win away from the NBA Finals. The 20-year-old Herro scored a Heat rookie-record 37 points and Heat beat Boston Celtics 112-109 on Wednesday night in Game 4 of the Eastern Conference finals.

“He has a great competitive humility about him,” Heat coach Erik Spoelstra said. “He has confidence. He has a fearlessness that is uncommon. But he’s humble enough to work, to be coachable, to take the mentorship from the veteran players that we have on our team, and he just continues to gain more confidence as we go.”

Jimmy Butler scored 24 points, Goran Dragic added 22 and Bam Adebayo – dealing with a bit of shoulder soreness – had 20 points 12 rebounds to help Heat take a 3-1 lead in the best-of-seven series. They can close it out tonight in Game 5.

Jayson Tatum scored all 28 of his points in the second half for Celtics. They erased a double-digit deficit to take a one-point lead in the fourth, then saw the Heat run away again. Jaylen Brown scored 21 points,  Kemba Walker added 20, Gordon Hayward had 14 and Marcus Smart finished with 10 points 11 assists.

“I didn’t score in the first half. That’s unacceptable,” Tatum said. “I know I have to play better. That’s what I tried to do.”

Brown’s 3-pointer with 16 seconds left cut Miami’s lead to 107-104. Herro went to the line 2.1 seconds later and coolly swished a pair, stretching the lead back to five. Celtics got within two points twice, Butler made a free throw with 1.1 seconds remaining, and Boston – out of timeouts – never got a desperation shot off.

“At the end of the day, we got to find a way,” Walker said. “That’s really all we can do. We can do it. It’s about pride. It’s about wanting to do it. Next game we got to come out and show that.”

Herro made 14 of 21 shots from the floor, 5 of 10 from 3-point range and became just the second 20-year-old in NBA playoff history to score at least 37 points in a game. The other: Magic Johnson, who had 42 in Game 6 of the 1980 NBA Finals for Los Angeles Lakers.

“I feel good about it,” Herro said. “There’s a lot of work to be done still. We’re up 3-1.”

Heat rookie playoff record was 27 by Dwyane Wade in 2004; it now belongs to Herro, who scored 17 points in the fourth alone.

Daniel Theis scored with 8:44 left to put Boston up 85-84, Celtics’ first lead since 25-24 with 11:19 left in the second quarter. It was Boston’s only lead in the second half and it lasted just 16 seconds.

Adebayo scored to give Miami the lead, and Herro basically carried the load from there.

“Herro’s shot-making tonight was the difference in the game,” Celtics coach Brad Stevens said. “Jimmy was great late. Adebayo was his typical self. Dragic made some big plays. But Herro was ridiculously good tonight. That rim must have looked like the ocean to him.”

Celtics shot exactly 8-for-20 in each of the first two quarters and that, combined with 11 turnovers, helped Heat go into the break with a 50-44 lead.

But Tatum’s first basket after a 0-for-7 start sparked what became a 6-for-7 finish to the third quarter for him; he had 16 of Boston’s 32 points in that period and Celtics were within 77-76 going into the fourth.

Heat, behind their youngest player, wouldn’t fold.

“Nothing Tyler does, surprises me,” Adebayo said.