Jay Fiedler, who completed 13 of 17 passes, threw for 203 yards and a touchdown.
Sammy Morris ran for 83 yards and a TD for the Dolphins, who entered the game as the NFL's only winless team.
The Miami offense looked solid against the Rams as Chris Chambers caught three passes for 128 yards and a touchdown and Randy McMichael had 78 yards and a TD on four receptions.
Marc Bulger hit 23 of 39 passes for 295 yards and a touchdown for the Rams (4-3). Marshall Faulk rushed for 61 yards on 12 carries and gained 74 yards on eight receptions. Isaac Bruce gained 98 yards on five receptions.
2014: NFL Cheerleaders [PHOTOS]
Julius Randle breaks leg during NBA debut