Drew Brees threw for 413 yards and four touchdowns as host New Orleans remained unbeaten and handed Miami its first loss.
Darren Sproles had seven catches for 114 yards and a TD and also ran for a score while tight end Jimmy Graham snared touchdown strikes of 27 and 43 yards from Brees, who tied his own NFL record with his ninth consecutive 300-yard performance.
Brees finished 30-of-39 to equal his own league mark with his 10th straight game of at least 25 completions for the Saints (4-0). Ryan Tannehill completed 22-of-35 passes for 249 yards and a touchdown, but he also had a key fumble and threw one of his three interceptions in the opening half as the Dolphins (3-1) failed in their bid for their first 4-0 start since 1995.
Lamar Miller rushed for 62 yards and a TD for Miami, which saw the game get out of hand when it allowed 21 unanswered points bridging halftime. The combination of Sproles and two turnovers by Tannehill helped the Saints to a 21-10 halftime lead. Sproles had a 48-yard reception to set up his own 5-yard scoring run and Graham made a leaping catch in the end zone for a 14-3 advantage midway through the second quarter.
Miller capped an 81-yard drive with a 5-yard TD run to make it 14-10 with 3:35 left in the half, but Tannehill was picked off by Jabari Green on the ensuing possession and Brees capitalized with a 13-yard scoring pass to Sproles.
After Miami went three-and-out to start the second half, Brees connected with Benjamin Watson and Graham on a pair of scoring strikes 92 seconds apart to turn it into a 35-10 rout.