Durant, the MVP of the Finals, had 39 points, and Curry added 34 for the Warriors, who captured the best-of-seven series 4-1 against the defending champions.
The two teams have contested the past three finals.
The Cavaliers are the clear-cut second-favorites to win next year's title, at 3-1 at the SuperBook.
For the Cavs, James added 13 rebounds and eight assists to his huge scoring night, while Kyrie Irving scored 26 and JR Smith had 25, but Kevin Love went missing, managing just six points from only eight shots.
"It's a time to definitely show everything that you're made of in those moments", Irving said Sunday on the eve of another elimination game with Cleveland trailing the Warriors 3-1 in the NBA Finals. This is a different year, a different situation, and, as Curry said, a different team - one with more experience, and with Kevin Durant.
Curry fared just fine in the first three games: 28.7 points, 9.7 rebounds and nine assists (yes, Curry was nearly averaging a triple-double just like LeBron James), all while hitting about 48 percent of his 3-pointers.
The Warriors became the first Bay Area professional sports franchise to clinch a championship on their home soil since 1974, and Durant was the X-factor who helped lead Golden State to the promised land. A 15-6 run led by six points from Irving got them within five, and after the Warriors pushed it back to 10, the Cavs scored six straight points, with Thompson's dunk cutting their deficit to 90-86. They get more calls, are able to complain to the officials, and get the benefit of the doubt- most of the time. If they let Cleveland in the back door, Golden State could be in big trouble.
It was the third year in succession the two teams had met in the finals.
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The Cavs' 37-33 lead through one quarter was their first lead at the end of any period in any game at Oracle Arena this season. The face value price is unknown, though some courtside seats cost $3,000, ESPN reported, citing a document that the Warriors sent fans previous year. Klay Thompson also did not step up the plate in the crucial match, and they will be hurt with their loss.
Durant shot 14 for 20 and Curry - the two-time reigning MVP who took a backseat as the new big star got acclimated - finished off a brilliant postseason.
"I've got the best team behind me", Thompson told Doris Burke matter of factly.
"We learned from everything we've been through", Curry said.
The Golden State Warriors have gained redemption, capturing their second National Basketball Association title in three seasons.
Green had sat out this very game a year ago, suspended because of flagrant foul point accumulation after he swiped at James' groin in Game 4.
Golden State turned this game on its ear with a 21-2 run over a 4:30 stretch in the second quarter.
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