Anthony took the ensuing inbounds pass from Kenyon Martin and answered with a 3-pointer of his own from the corner with 0.1 seconds left, capping a 31-point performance in the Nuggets' 122-120 victory Friday night.
"I want to get out of town before the sheriff catches us for stealing," Denver coach George Karl said. "He has made some big shots for us. Durant made an incredible shot and Melo made one right on top of him. Somehow that's how the NBA works on some nights. Great players do great things."
Denver (22-12) trailed Oklahoma City (4-30) by 14 points in the second half as the Thunder appeared set to record consecutive wins for the first time this season. But the Nuggets' trio of Anthony, Chauncey Billups and Nene kept that from happening.
Nene had 27 points on 10-of-11 shooting and 14 rebounds, and Billups added 24 points for Denver, which was playing on the road for the eighth time in 11 games.
Meanwhile, the Thunder lost on a last-second shot for the third time this season, having fallen in similar fashion to the Minnesota Timberwolves and Detroit Pistons.
"That team is not a four-win basketball team," Billups said.
Durant led the Thunder with 33 points, and Jeff Green had 18. Oklahoma City shot a season-high 58.4 percent from the field and posted its highest point total of the season, but Denver answered with 54.7 percent shooting.
Anthony's winning shot, well-guarded by Oklahoma City's Desmond Mason, was Denver's fifth 3-pointer of the fourth quarter.
"That was a heck of a game," Oklahoma City coach Scott Brooks said. "Nobody deserved to lose that game tonight. It should've gone into overtime after overtime. Carmelo hit a great, tough, competitive shot. Desmond got his hand up on the jump. It was a tough shot.
"Their best players had 27, 24 and 31. That's what it takes to beat us in our building."
Billups' 3-pointer with 1:45 left broke a 113-113 tie, and Oklahoma City didn't regain the lead until Durant's shot with 2.7 seconds left, when he took a pass from Green and hit his fourth 3-pointer in five attempts.
"I told myself I wanted the ball," Durant said. "I wanted to hit the game-winner."
For a few moments, it appeared he had done so. But after a Denver timeout, Anthony approached Martin, who was to inbound the basketball, and told Martin to look for him on a play designed for either Anthony or Billups.
"I knew that 2.7 seconds was a lot of time," Anthony said. "I tried to catch it closer to the basket but I knew that I could still get to the basket in 2.7 seconds. Kevin stood there and looked at me and I had a chance to look at his feet and I just shot it."
The crowd at the Ford Center, rollicking before the play, quickly fell silent.
"I couldn't believe he made it," Durant said. "I still can't."
Denver led by 11 points in the first period and maintained that lead through much of the half.
But Oklahoma City responded with its highest-scoring quarter of the season, scoring 38 points. Denver was up 49-48 after a dunk by Martin with 4 minutes left in the half, but the Thunder went on a 16-4 run before halftime to take a 64-53 lead. Earl Watson keyed the spurt, scoring four baskets and assisting on another.
The Thunder's previous high for points in a quarter this season was 34, and their best first-half point total had been 55, four days earlier in a loss to the Phoenix Suns. Oklahoma City went 17 of 25 from the field (68 percent) in the second quarter as the Nuggets committed eight turnovers.
Oklahoma City led 74-60 after a three-point play by Robert Swift with 9:52 left in the third quarter. Denver closed to 92-89 on Billups' 3-pointer with 46.5 seconds left in the quarter, but the Thunder scored the next six points to rebuild their advantage.
Anthony's two free throws with 3:50 left put the Nuggets up 109-107, their first lead since the second quarter.
Martin added 13 points for Denver. Wilkins had 16, and Watson added 15 points and seven assists for Oklahoma City.
Denver forward Chris Andersen received applause when he checked in for the first time with 3:38 left in the first quarter. Before he was suspended from the league in January 2006 for violating its substance abuse policy, Andersen was a fan favorite when the New Orleans Hornets played in Oklahoma City. ... Oklahoma City forward Nick Collison sat out for the fifth time in the past six games with a fractured thumb. He's listed as day-to-day.