Kevin Durant scored 32 points to extend his lead in the NBA scoring race, leaving Kobe Bryant in need of 38 points in his season finale Thursday night against Sacramento to claim his third scoring title and prevent Durant from becoming the seventh player to win three in a row.
Both are averaging about 28 points per game.
LeBron James, who has sat out two of Miami's last three games to rest, would need to score 83 in his finale to have a chance.
Lawson's free throw with 4:11 remaining put Denver up 96-95, and the Nuggets wouldn't trail again.
With a win Thursday at Minnesota, Denver would be the No. 6 seed and face the Los Angeles Lakers in the first round of the playoffs. If the Nuggets lose and Dallas wins at Atlanta, Denver would fall to No. 7 and have a rematch with Oklahoma City. The Thunder beat Denver 4-1 in the first round of last year's playoffs.
Durant had downplayed the importance of winning the scoring title, but the Thunder at least gave him a fighting chance to win it down the stretch.
Durant sat out the fourth quarter after playing 32 minutes in a close game against Sacramento a night earlier, but this time he returned with just over 8 minutes left after Denver had scored eight straight points to go up 88-86 following Lawson's driving layup.
Durant had scored only 25 points by then - meaning Bryant would have needed only 32 to win the title.
Just after returning, Durant tied the game with a two-handed dunk off an alley-oop from Westbrook, but the Nuggets came right back with the next six points to push their advantage to 94-88 after Faried's reverse layup with 6:09 remaining.
Durant responded with a 3-pointer and Oklahoma City tied it at 95 after Westbrook's two free throws with 4:27 to go. Lawson scored the next three points on free throws and Denver hung on from there.
Durant negated a possession with Oklahoma City trailing 100-99 when he was called for an offensive foul. Faried grabbed Arron Afflalo's missed shot and dunked it with two hands before Russell Westbrook missed a 3-point attempt for the tie.
Corey Brewer then got around Derek Fisher and banked in a critical 18-footer as the shot clock expired to bump the lead to 104-99.
The Thunder had one last chance to tie, but Fisher missed a 3-pointer from the left wing with 9 seconds left.
Westbrook finished with 30 points, and Serge Ibaka had 15 points and four blocks for Oklahoma City. Both had injury scares in the second half, with Ibaka leaving the floor with a hip contusion and Westbrook coming down hard on his left wrist after trying to block one of Brewer's shots.
Afflalo added 15 points for Denver, which had seven players in double figures.
Notes: The Thunder unveiled their Northwest Division championship banner before the game, waiting until a divisional opponent played at Chesapeake Energy Arena to do it. Oklahoma City clinched its second straight division title on April 8. ... Durant said he was proud of achieving his preseason goal of playing in all 66 games. It's the second time in his five-year NBA career that he played every game. ... The only players to win at least three straight scoring titles are George Mikan, Neil Johnston, Wilt Chamberlain, Bob McAdoo, George Gervin, and Michael Jordan. Chamberlain and Jordan are the only ones to have more than three in a row, with both winning seven consecutive titles.
(Copyright 2012 by The Associated Press. All Rights Reserved.)