The Nuggets led by four with 4:28 to go before Hamilton, who finished with 13 points, made three 3s in a span of 67 seconds to push Denver's lead to 11. Nate Robinson led the way with 20 points for the Nuggets (12-8), who were playing their fourth game in five nights and had dropped their previous two.
Tony Wroten finished with 20 points for the Sixers (7-14), who held a four-point lead at the half. Philadelphia has dropped 10 of 12.
Denver dominated from beyond the arc, where it hit seven 3-pointers to the Sixers' three, and on the boards, where it won the rebounding battle 52-38.
Both teams played without their starting point guards.
Ty Lawson, who left Denver's 106-98 loss to the Boston Celtics on Friday, was sidelined with a left hamstring strain. The fifth-year pro leads the Nuggets in scoring (19.3) and assists (8.0).
Sixers rookie Michael Carter-Williams spent his third night in the hospital while recovering from an infection on his right knee and missed his second straight game.
"It's being monitored closely, but nothing to get too overly concerned with," Philadelphia coach Brett Brown said before the game.
Philadelphia is 1-5 this season without Carter-Williams.
The Sixers jumped out of the gate quickly on a 10-2 run. Denver took its first lead 23-22 with 1:53 in the first, but Hollis Thompson's 3-pointer with 47 seconds to go sparked Philadelphia to a 27-25 advantage after 12 minutes.
The fifth game of a six-game road swing might have taken its toll on the Nuggets, who have been plagued recently with slow starts and trailed after the first quarter for the fifth straight game.
Philadelphia played an unusually clean first half in which it turned the ball over just four times to take a 53-49 lead into intermission. One of the league's worst in turning over the ball, the 76ers entered averaging 18 giveaways per night.
Wroten started in Carter-Williams' place and led the way at the half with 14 points on 7-for-12 shooting. As a team, the Sixers shot 50 percent from the floor before halftime. Robinson (12 points) and Randy Foye (11) paced the Nuggets, who shot 39 percent.
NOTES: Lawson did not play for the first time this season. The Nuggets were 8-1 last year without Lawson in the lineup. ... Saturday was the first of two meetings between the teams this season. Denver will host Philadelphia on Jan. 1. ... The 76ers observed a moment of silence prior to the game for South African leader Nelson Mandela, who died Thursday at 95. ... On Monday, the Nuggets wrap up their six-game road trip at the Washington Wizards and the Sixers host the Los Angeles Clippers.