A.J. Feeley, who passed for 176 yards and a touchdown, directed the game-winning, 40-yard drive inside the final two minutes.
Randy McMichael caught nine of Feeley's passes for the Dolphins (4-11), who improved to 3-3 under interim Coach Jim Bates.
The win came a day after Miami reached an agreement with Louisiana State's Nick Saban to take over the team for the 2005 season.
For the Indians (3-12), Lee Suggs ran for 143 yards and broke Jim Brown's 45-year franchise record with 38 carries in Cleveland's ninth loss in a row.
Celebrity Families of 2014 [PHOTOS]