The one-sided defeat ended the Patriots' 21-game regular-season winning streak.
Brown, who totaled 113 yards rushing, ran for touchdowns of 62, 2, 5 and 15 yards and connected with Anthony Fasano on a 19-yard scoring pass.
Quarterback Chad Pennington completed 17 of 20 passes for 226 yards for Miami (1-2).
Miami gained 461 total yards to 216 for the Patriots.
Matt Cassel was 9 of 31 passing for 131 yards and a touchdown for New England (2-1),
Swim Week Miami Beach 2014 [PHOTOS]