Dorsett had scoring grabs of 4 and 32 yards from Brad Kaaya for the Hurricanes (1-1), who beat the Rattlers for the ninth straight time. Johnson had 97 yards on nine carries, including a 1-yard scoring run, and Gus Johnson ran 15 yards for another Miami touchdown.
The win came in the 100th game of Miami coach Al Golden's career, evening his record at 50-50.
Kaaya completed 12 of 22 passes for 177 yards, with the two touchdowns and two interceptions. Miami's Trayone Gray had a 10-yard touchdown run - on the first carry of his career - with 4:17 left.
John Boston recovered a botched punt snap in the end zone for Florida A&M (0-2). Brandon Norwood had 74 yards on three catches for the Rattlers.
Florida A&M brought its famed band down from Tallahassee, and the ''Marching 100'' - as expected - put on a scintillating show at halftime, replete with the performers lining up in a ''305'' formation, a nod to the primary area code in the Miami area.
By then, though, the game was decided.
The Hurricanes got touchdowns on four of their first six possessions, rolling out to a 28-0 lead late in the first half. There were 27 plays in the first quarter, with the line of scrimmage on every one - regardless of who had the ball - being in Florida A&M territory. Miami opened drives on the Rattlers' 49 twice and another on their 13.
Dorsett's 4-yard touchdown opened the scoring. His 32-yard catch in the back of the end zone late in the half made it 28-0, with Dorsett diving near the end line and staying in bounds.
Johnson had a 1-yard run for Miami's second score, and his 55-yard carry highlighted the drive that was capped by Edwards' touchdown and pushed Miami's lead to 21-0.
Johnson has played in 22 games for Miami, with rushing touchdowns in 12 of them. Miami is now 12-0 in those games.
It was Johnson's first home game since Oct. 26, after his 2013 season ended early because of a broken ankle suffered at Florida State. His family obtained more than 100 tickets to Saturday's game - ''Return of the Duke,'' they called it - for friends and relatives. They saw him climb up the Miami all-time lists, passing Edgerrin James for No. 5 in all-purpose yards and Frank Gore for No. 9 in career rushing by a Hurricane.
Johnson now has 2,047 rushing yards at Miami.
Dorsett's two touchdown catches matched a career-best - his other 2-TD game coming against North Carolina State in 2012.
Miami got many of its first-stringers out before the third quarter ended. Johnson's night was over by halftime and Kaaya was replaced by senior transfer Jake Heaps in the third quarter.
The Hurricanes improved to 179-4 since 1985 when scoring at least 31 points.