The Dolphins defense did a splendid job in the second half, intercepting Brady twice and sacking him two more times, but by then the damage had been done.
The final score might have been closer had the Dolphins been able to cash on two first-and-goal opportunities that came up short.
The second time was in the third quarter when Lemon tried to scramble into the end zone on fourth-and-goal but stepped out of bounds just before reaching the pylon.
The Dolphins finally broke through on their next possession, with Lemon connecting with Greg Camarillo, the hero of last week's victory over Baltimore, on a 21-yard touchdown pass.
But the Dolphins offense could do nothing in the last quarter-plus, as Lemon faced constant pressure and the receivers couldn't get open.
The start of the game was a disaster for Miami, as the offense went three-and-out and the defense then allowed a 71-yard touchdown drive that ended with Brady's 10-yard pass to Moss.
Maroney's 51-yard run set up Moss' second touchdown, which came on a 1-yard pass.
The Maroney broke loose on a 59-yard touchdown run on third-and-1 before Brady connected with Jabar Gaffney on a 48-yard touchdown pass to make it 28-0.
Safety Lance Schulters was in pretty position to make the interception on the play as he sprinted to the sideline from his safety position, but the ball went through his hands and right to Gaffney, who had nothing but open field after making the catch.
The loss clinched the first overall pick in the 2008 draft for the Dolphins, while the Patriots stayed on course for the first 16-0 regular season in NFL history.