Javonte Williams scored his second touchdown of the night, a 5-yard run with 5:53 remaining in the third quarter to give the Broncos a 26-3 lead on the Saints.
The Broncos have scored on six consecutive possessions since punting on the opening drive.
They led 16-3 at halftime.
Williams has rushed for 81 yards on 12 carries and caught three passes for 23 yards.
Rookie quarterback Bo Nix has run for 73 yards on nine carries, while completing 15 of 24 passes for 161 yards.
The Broncos have outgained the Saints 357 to 164.
The Saints lost another player to injury, with guard Nick Saldiveri ruled out with a shoulder injury.
