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 first time in six years.
The Warriors went ahead by 18 points early in the fourth before holding off one final Nuggets flurry.
Andre Iguodala scored 24 points and Ty Lawson had 17 in another disappointed 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 hot-shooting Warriors.
NETS 95, BULLS 92
CHICAGO (AP) — Deron Williams, Brook Lopez and Joe Johnson each scored 17 points, and Brooklyn again avoided elimination, beating short-handed Chicago to tie their first-round series at 3.
The series goes back to Brooklyn for Game 7 on Saturday, with the winner getting defending champion Miami in the second round.
The Bulls hung in until the end even though they were missing Luol Deng and Kirk Hinrich, but Brooklyn came away with its second straight win to avoid elimination.
Marco Belinelli started at shooting guard with Jimmy Butler moving to small forward and scored 22 points. Robinson started his second straight game with Hinrich injured and finished with 18 points. Butler had 17 points, seven rebounds and six assists.
Noah added 14 points and 15 rebounds. Carlos Boozer scored 14 and grabbed 13 boards.