Andre Iguodala scored 24 points and Ty Lawson had 17 in another disappointing early exit for Denver, which has lost in the first round nine of the past 10 seasons.
The Nuggets won 23 of their final 26 regular-season games to earn the Western Conference's third seed, then lost four of six to the Warriors.
Golden State only outshot the Nuggets 40.3 percent to 34.7 percent in the finale but dominated the rebounding matchup again, 55-44. The Warriors overcame 21 turnovers including 10 in the fourth.
Golden State will open the second round at San Antonio on Monday. The Spurs swept the Lakers in four games.
Curry connected all over his home court in another dazzling second half. Curry swished all four of his 3-pointers in the third quarter and brought the sellout crowd of 19,596 roaring each time.
He also dribbled behind his back and through his legs, crossing over Lawson and zipping a pass through traffic to Bogut for a thunderous dunk. With Denver starting to chase Curry around the perimeter, the spacing started to open up.
Curry added a one-handed pass off the dribble to a cutting Carl Landry, who finished for a three-point play over Wilson Chandler, flexed his arms above his shoulder and belted out a roar from the floor to give Golden State a 64-53 lead.
Green made a corner 3 in front of Denver's bench, and Klay Thompson hustled for a rebound and a quick put-back to put the Warriors up 80-62 with 9:11 to play.
The Nuggets failed to score for nearly six minutes during the stretch. But they rallied with 13 straight, held the Warriors scoreless for almost five minutes and gave the fans in Oakland reason to worry.
After the Warriors went back ahead by nine, they had 10 turnovers in the fourth and nearly collapsed. Chandler stole the rebound from Green for an easy layup to get within four, Iguodala hit another from long range and Kenneth Faried made 1 of 2 free throws to bring Denver within two with 32.4 seconds to play.
Iguodala stole Thompson's pass on the ensuing play. Chandler's running layup rimmed out, he missed a put-back and then knocked the ball out a call that stood after a video review.
The Nuggets were forced to intentionally foul Jarrett Jack, who made both free throws to give Golden State a 92-88 lead with 7.3 seconds remaining to seal the victory.
Golden State seemed to have an answer for everything .
Even All-Star forward David Lee made a surprising return for the Warriors after not dressing the previous four games with what the team had called a season-ending hip injury. He grabbed one rebound and missed one jumper in 87 seconds off the bench in the first quarter.
Storylines Warriors 92, Nuggets 88
R Golden State builds an 80-62 lead, then fends off Denver's rally for the series-clinching win.