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.
That included Durant's stop just outside the restricted area under the basket.
"Down the stretch, it seemed like they got every whistle possible and that really changed the tide," San Antonio's Tim Duncan said. "We were playing tough defense and trying to get stops, but the whistle kept blowing and they went to the line."
Tony Parker finished with 29 points and 12 assists, but only eight of the points and two assists came after San Antonio took a 63-48 halftime lead. Duncan chipped in 25 points and 14 rebounds, and Stephen Jackson hit six 3-pointers and scored 23 points.
The Spurs had won 20 in a row, moving past the Thunder for home-court advantage in the West and then taking a 2-0 lead in the series, before losing four in a row.
"There's not much to complain about," Ginobili said. "We had a great run. We just couldn't beat these guys."
Durant grabbed the final rebound, dribbled the ball across half court and raised his right fist to celebrate with a sold-out crowd wearing free white T-shirts. The franchise will play for the NBA title for the first time since 1996, when it was in Seattle.
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.