Durant, the second- overall pick in last year's draft and the leading candidate for rookie of the year, scored a season-high 37 points and Green, the fifth pick, had a season-high 35 to lead the Sonics to a 151-147 double-overtime victory over Denver on Sunday night.
"My teammates were making plays and I was just there finishing them," Green said.
The loss kept the Nuggets (46-31) in a tie with Golden State for the eighth and final playoff spot in the Western Conference. The Warriors lost to New Orleans, 108-96, earlier Sunday.
"Career nights from two people," Denver's Allen Iverson said. "You have two 30-point scorers and other guys doing what they did out there, what can you say? They were the better team tonight."
Green, whose previous high was 23 points, scored 24 in the second half and overtimes. His five quick points to start the second overtime gave the draft lottery-bound Sonics (18-59) the winning cushion.
Durant was coming off his worst shooting night of the season, going 2-for-17 to finish with four points in a loss to Houston on Friday night.
The loss was against a team that the Nuggets' had beaten three times this season by an average of 37 points. Just three weeks ago, the Nuggets routed the Sonics, 168-116. The 52-point victory margin was the widest in Denver and the Nuggets point total was the highest in the NBA this season.
"We owed those guys," Durant said. "They came beat us badly the last two times."
This was the first of four straight road games for Denver. They visit the Clippers Tuesday, Golden State on Thursday and Utah Saturday. The Nuggets dropped to 16-22 on the road, the worst among the West's postseason contenders.
"We've got to get all three of them," Nuggets guard J.R. Smith said. "We got to beat Golden Sate because they're right on our heels. We owe Utah and we got to beat the Clippers just to stay ahead.
"If we don't play, we'll be sitting at home watching the playoffs."
Seattle, which led by six at intermission, had an 11-point lead until a 17-9 run by the Nuggets pulled them to 86-83 with 4:39 left in the third.
However, an alley-oop dunk -- plus a free throw -- by Green, on a pass from Durant with 4:12 left charged up the crowd. The Sonics rode that momentum, holding off the Nuggets to maintain a 99-95 lead enter the fourth quarter.
The Nuggets finally went ahead for the first time in the second half, 105-103, on a fastbreak basket by Smith with 9:26 left. The lead then changed hands seven times and was tied four times over the final 9 minutes of regulation.
Linas Kleiza's 3-pointer with 1:06 left gave the Nuggets a 126-123 lead. Coming out of a timeout, Durant answered with a 3 from the top of the key with 22 seconds left to send the game into overtime.
Green scored 14 of points in the fourth.
Neither team led by more than five points in the first overtime. Anthony hit a 24-footer with 1:37 left for a 132-130 lead. Green's shot was then blocked by Marcus Camby. Iverson followed with a 3-pointer from the right side for a 135-130 lead with 1:01 left.
After Durant hit a pair of free throws with 32.1 seconds left to make it 135-132, Iverson missed 22-footer from the left side with 11.9 seconds left. After a timeout, Durant hit a 30-foot 3 with 5.1 seconds left to tie the score.
Martin miss a 24-footer as time expired to force a second overtime.
Held to a season-low 66 points Friday, the Sonics had their most points in a half this season, leading 70-64 at the break.
"They played with a ton of heart and they didn't give in," Sonics' coach P.J. Carlesimo said. "They competed. I just thought it was a great effort."
The Sonics need to win all of their final five games just to match their franchise-low mark of 23 wins set in their inaugural season of 1967-68.
Entering the game, the Nuggets had won the first three meetings over the Sonics by an average of 37 points. ... The Sonics play three straight road games in Texas this week, including Friday in San Antonio. It will be the team's first visit to San Antonio, where Sonics coach P.J. Carlesimo was an assistant last season. ... Nuggets coach George Karl said before the game that there was no comfort in the fact that Denver had dominated the Sonics this season. "There's never this [large] of a gap between NBA teams. It just doesn't exist," he said. "The truth of the matter is all NBA teams are fairly bunched together. They're a capable NBA team."