CLEVELAND — The NBA Finals should sweep the ratings for late-night dramas.

For the first time in league history, the first two games both went to overtime. Game 3 Tuesday night didn’t need extra time, but the drama faucet was dripping again.

The Cleveland Cavaliers almost blew a 20-point lead in the third quarter, but hung on to defeat the Golden State Warriors, 96-91, at Quicken Loans Arena. The win gave the Cavaliers a 2-1 lead in the series.

The Cavaliers never trailed in the game, but sparked finally by some scoring from NBA MVP Stephen Curry, Golden State came back and sliced the lead to 81-80 with 2:46 to play. But after a three-point play from Matthew Dellavedova and a 3-pointer by LeBron James, Cleveland opened up an 87-80 lead — and Golden State melted down the stretch. Curry had three crucial turnovers in the final three minutes, one on a behind-the-back pass.

Still, his 3-pointer with 18 seconds left made it 94-91. James clinched the win with two free throws with 16.8 seconds left.

James came close to his second consecutive triple double as he finished with 40 points, 12 rebounds and eight assists. He averaged 41 points, 12 rebounds and eight assists the first two games.

Golden State coach Steve Kerr was asked if James was the best athlete he had ever seen, regardless of sport.

“Can you find another one?” said Kerr. “Maybe American Pharoah?”

James played all but two minutes of the game.

Cleveland coach David Blatt said, “He understands the moment. He understands the situation, and he is a big, big, big-time player.”

James’ 123 points is the most in the first three games of NBA Finals history. It was the third consecutive game he took at least 35 shots.

“LeBron is not the issue of why we are down 2-1,” said Curry. “It’s the way we’re playing on offense and at the start of games.”

Golden State shot only 40 percent from the field and 35 percent from 3-point range. Andre Iguodola scored 15 points off the bench and Klay Thompson 14. David Lee also gave a lift off the bench and helped the comeback with 11 points.

For Cleveland, Dellavedova, the kid from the Land Down Under, is playing up and over the top.. He finished with 20 points and once again hounded Curry for most of the game. Curry had 27 points, but only three in the first half. He finished 10 of 20 from the field and 7 of 13 from 3-point range.

Tristan Thompson had 10 points and 13 rebounds for Cleveland. J.R. Smith had 10 off the bench for a Cavaliers team that shot 43 percent (9 of 21) from 3-point range.

Quicken Loans was a deafening mad house throughout the night with fans hoping the Cavaliers would seize control of the series and move within two wins of giving the city its first championship in any sport in 51 years, when the Browns won the NFL title. History says it was a monumental win for the Cavaliers. Teams that won Game 3 in a 1-1 series have gone on win the NBA title 31 of 37 times. And it was yet another win without Kyrie Irving, who sustained a fractured kneecap in Game 1, and Kevin Love, who hasn’t played since the first playoff series because of an injured shoulder.

Also, starting guard Iman Shumpert sustained an injured shoulder in the first quarter, although he returned to the game.

“Man, this is a resilient group,” said Blatt. “They just don’t give in. If you can bend and not break, you’ve always got a chance.”

Cleveland scored the first basket of the game and Golden State never got even the rest of the game.

Cleveland led at halftime, 44-37, and Dellavedova and James stepped on the gas at the start of the third quarter and the Cavaliers ran away from the Warriors. Cleveland had a 68-48 lead with 2:52 left in the quarter. Cleveland took a 72-55 advantage into the final quarter and Golden State looked more like Listless State. Curry got a basket with 6:20 left in the third, his first points since he scored Golden State’s first basket of the game.

“I didn’t like our energy. I didn’t like our body language for much of that first three quarters,” said Kerr. “This is what we have to fight through. Things aren’t going our way, it doesn’t matter, you’ve got to fight through. You’ve got to bring energy.”