Bradley Beal ended with 21 points, seven boards and two steals for the Wizards, who went 1-3 on a four-game road trip. Trevor Ariza and Marcin Gortat donated 18 and 16 points, respectively, with Gortat also pulling down 10 boards.
With the score tied at 84 with 7:51 to play, the Nuggets went on a 7-0 spurt. Evan Fournier made two straight baskets before Arthur's 3-pointer.
Washington got within 94-91 on Gortat's tip-in with 5:19 remaining, but John Wall was called for a charge on the Wizards' next trip down the court.
Faried's alley-oop slam and Brooks' jumper made it a 98-91 contest. Denver went 7-of-8 from the foul line down the stretch to seal the victory.
Earlier, Ariza scored 15 points in the first quarter to give the visitors a 29-21 edge after 12 minutes.
Denver used a 9-0 run late in the second stanza to grab a 45-43 lead. The Wizards, however, closed out the half on a 6-2 spurt to take a 49-47 margin into the locker room.
The Nuggets closed out a tight third frame with six straight points. Brooks' layup with 2.9 seconds left made it 77-73 in favor of Denver.