Golden State can make history as the first team to sweep the playoffs if they win Game 4 on Saturday, Manila time.
Durant finished 31 points and eight rebounds, with guard Klay Thompson adding 30 points in a breakout performance after two weak games to start the series.
Irving bounced back from a rough Game 2 with 38 points, including a couple of dazzling layups where he juked around multiple Warriors.
Golden State sank an NBA Finals record nine 3-pointers in the first quarter, four of them by Thompson, who scored 16 points in the opening period.More news: With time running out, Florida Legislature remains split
The Warriors trailed by six with three minutes left before Durant, who signed with Golden State last summer to win a championship, brought them back, scoring 14 in the fourth.
For the Warriors, a win will make them the first National Basketball Association team to get through the playoffs with four series sweeps, 16-0.
"All I was looking at was the bottom of the net", Durant said.
"I've been wokring on that shot my whole life, and for that one to go in, that's liberating", the forward told ESPN's Doris Goodwin after the game.
THE Cleveland Cavaliers had a win in their grasp and watched it fade away. but don't blame LeBron James. I don't contribute as losing this game because we got exhausted. "I think we have grown and matured just mentally of how to just pace yourself through this long year and take every day as a new experience and something that you can kind of take control of".More news: No bond for woman accused of leaking top-secret documents
The thrilling back-and-forth affair was the first close game of the finals, but the Cavaliers will now have to do what no National Basketball Association team has ever done in the playoffs, win four straight games after going down 0-3 in a series.
"It's the most firepower I've played in my career", said James, who played all but two minutes. I played against some great teams, but I don't think no team has had this type of firepower. "Came down to the stretch, and they made some big-time plays".
They're just not good enough to beat what may be one of the NBA's best teams ever. If some of his fellow Cavs (James and Irving aside, of course) can do the same on Friday, well, they'll nearly certainly still lose the series, but at least they will have averted a scenario many are now predicting: "Warriors in 4". "We missed some shots, and they made some".
Showing off his ability to spin in shots high off the backboard, Irving scored 16 in the third quarter and the Cavs held the Warriors to 22 points in their lowest scoring output in any quarter in this postseason.
But I was able to get second and third and fourth winds. But the Warriors were that much better, going 16-for-33 from deep.More news: Rajasthan Board Class 10 Result 2017 On 8 June At 4 PM