Andre Bogut had season-bests and career-playoff highs of 14 points and 21 rebounds, and rookie Draymond Green added a career-high 16 points and 10 rebounds to power Golden State into the second round for the second time in 22 years.
The Warriors open the second round on Monday night in San Antonio.
"When we go in the locker room, we're jumping up and down, we're hugging, we're changed men," coach Mark Jackson said. "This is the greatest group of men as far as a team that I've ever been around or seen in my life."
Iguodala scored 24 points and Lawson had 17 to lead the Nuggets, who were unable to overcome the loss of Gallinari to the injury last month.
Denver shot 7-for-28 from 3-point range in Game 6 and made just 31 percent from long range for the series.
"We do miss him but we can't be worried about that," forward Kenneth Faried said. "We had to go out there and do what we had to do. Without him it is tough because he's our leading scorer."
The Warriors only outshot the Nuggets 40.3 percent to 34.7 percent in the finale but dominated the rebounding matchup again, 55-44. They also overcame 21 turnovers — including 10 in the fourth — while the Nuggets only had seven.
Jackson ratcheted up the rhetoric after the Nuggets won a physical Game 5, saying Denver sent "hit men" out to take "cheap shots" at Curry. The accusations earned Jackson a $25,000 fine from the NBA for an "attempt to influence the officiating," though neither side ever got out of control in the finale.
Except Curry's shooting — again
On the ball or off the dribble, 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 frenzies fans roaring to their feet each time.
Green also 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.
NOTES: 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. ... Aaron Hern, an 11-year-old from nearby Martinez, who was injured in the bombings during the Boston Marathon, attended the game with his family and honored on the videoboard during the first quarter.