The Dolphins were particularly impressive in the first half when they sacked Brady three times and came up with two takeaways.
The offense didn't light it up against New England and Ricky Williams needed more than 35 carries to reach the 100-yard mark, but it got the job done.
Jay Fiedler rebounded from a four-interception performance at Kansas City with a strong effort that included a nifty touchdown run and two TD passes, to Chris Chambers and Randy McMichael.
The Dolphins took control in the first half, charged to a 16-0 halftime lead and never led by less than 10 points in the second half.
New England appeared ready to make a charge after Williams fumbled on the first drive of the second half and the Patriots marched 68 yards for a touchdown that made it 16-6 (the two-point conversion failed). But the Dolphins defense forced a three-and-out on New England's next possession and the Dolphins basically slammed the door shut when Fiedler capped a 74-yard drive with a 1-yard touchdown pass to McMichael to make it 23-6.
For good measure, the Dolphins added a field goal after the two-minute warning after they recovered an onside kick that followed New England's second touchdown.
But this game clearly was won in the first half, despite the Dolphins missing an opportunity to take the lead on their first drive when Olindo Mare missed a 45-yard field goal attempt.
But the defense began making plays on New England's next series, with Jason Taylor forcing a fumble on a sack of Brady. Adewale Ogunleye recovered at the Pats 39 yard-line.
Nine plays later, on third-and-goal from the 8, Fiedler couldn't find anybody open and his protection began breaking down. But Fiedler was able to fight through a sack attempt and he sprinted to the right corner of the end zone for the touchdown.
After the extra point was blocked by Tebucky Jones, the Dolphins led 6-0.
They increased their lead to 13-0 early in the second quarter after Patrick Surtain intercepted Brady in New England territory. Actually, the play was made by Sam Madison, who left the man he was coverage and stepped in front of intended receiver Deion Branch.
Madison couldn't come up with the pick, but he tipped the pass in the air and Surtain came down with it.
The Dolphins originally had to settle for a Mare field goal, but New England's Tedy Bruschi was penalized for jumping off the back of a teammate and that gave Miami a first down.
Three plays later, Fiedler hit Chris Chambers in the back of the end zone for a 7-yard touchdown.
The Dolphins increased their lead to 16-0 in the final two minutes of the first half when Mare hit a 40-yard field goal.
By the end of the half, New England had managed a grand total of three first downs and 26 total yards.
New England was more competitive in the second half, but by then the Dolphins had done their damage.