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The Thunder, only three years removed from a 3-29 start that had them on pace for the worst record in NBA history, went through the only three West teams to reach the finals since 1998 — Dallas, the Los Angeles Lakers and San Antonio — to earn their shot at the title.

Game 1 of the NBA finals will be Tuesday night in Oklahoma City against either Boston or Miami. The Celtics lead that series 3-2 and can earn a trip to the finals with a win at home in Game 6 on Thursday night.

The Thunder took the lead for good early in the fourth quarter, getting nine of their first 13 points on free throws as the fouls started to pile up for San Antonio — six on the defensive end and three on the offensive end in the first 7 minutes.

Even Durant drew what he thought was his first charge of the season, stepping in front of Ginobili.

Derek Fisher and James Harden hit 3-pointers in a three-possession span to increase the lead to 99-93 with 3:13 remaining. Jackson, who had made his previous six 3-pointers, and Parker both missed 3s that would have gotten the Spurs within 103-102 in the final minute.

The Spurs put up quite a fight, at least for the first half.

Parker, who had been largely bottled up ever since the Thunder put 6-foot-7 defensive specialist Thabo Sefolosha on him in Game 3, had a hand in the Spurs‘ first 12 baskets, making seven on his own and assisting on the other five.

Kawhi Leonard and Jackson followed his three-point play by nailing back-to-back 3-pointers for a 34-16 advantage in the final 2 minutes of the first quarter.

“I told the coaches that I could go all night, I could go 48, and I didn’t think they would let me do it,” Durant said. “But they kept me in and I just tried to give my team a spark.”

The Thunder stormed back with an 11-2 run to start the third quarter and eventually pulled ahead after Durant’s 3-pointer from the top of the key made it 79-77 with 1:41 left in the period.

San Antonio missed nine of 11 3-pointers in the second half.

“The third quarter, it was like playing in mud,” Spurs coach Gregg Popovich said. “So, that was our downfall as much as anything.”

Notes: Popovich, whose request for his team to play nasty led to T-shirts being made in San Antonio, said at the morning shootaround that his team needed to play “with a little bit of ugly.” Not nasty? “I was trying to stay away from that word,” he said. … San Antonio had a 29-28 edge in the second quarter after getting outscored 138-106 in the period in the first five games — dropping more than six points per game. … Greg Willard was initially scheduled to be one of the three officials but pulled out due to illness. Rodney Mott replaced him, alongside Joe Crawford and Bill Kennedy.