Miami (4-1) beat the Patriots (3-2) for the sixth time in the last seven meetings.
"This is a great accomplishment," Fiedler said. "We beat the team that was in our way to take the lead in the AFC East. That made it a bigger game than them being Super Bowl champions.
"This win puts us on top and now we have to keep it going to separate ourselves from the rest of the pack."
After throwing four interceptions in a 48-30 loss at Kansas City last week, Fiedler hurt the Patriots with his legs as well as his arm.
When New England's secondary had Miami's receivers blanketed, Fiedler escaped a pass russ and scored on a 10-yard run with eight seconds left in the first quarter to give the Dolphins a 6-0 lead.
On third and goal at the New England seven, Fiedler ran a play-action fake with Williams, kept his poise in the pocket and fired a pass into the end zone to Chris Chambers 3:22 into the second quarter to increase the advantage to 13-0.
New England failed to score in the first half, but Brady connected with David Patten on a 34-yard touchdown to pull the Patriots within 16-6 early in the third quarter.
Fiedler, however, engineered a 10-play, 74-yard drive which featured a 35-yard bomb down the left sideline to James McKnight. Fiedler capped it with a one-yard scoring toss to rookie tight end Randy McMichael with 65 seconds left in the third, opening the lead to 23-6.
After being steamrolled by Priest Holmes for 180 yards two weeks ago and 217 yards by LaDainian Tomlinson last week, Patriots Coach Bill Belichick was determined to stop Williams with his defensive scheme.
Williams rushed for 105 yards on 36 carries, an average of less than three yards per carry, and also committed a fumble that led to New England's first touchdown.
"They always had eight guys in the box and we knew they were going to do that," Williams said. "They were blitzing the gaps and making sure that there weren't any lanes for us to run through. They did a good job, but Jay came up big and played well on third downs. He kept the chains moving and kept the clock ticking."
Thanks to solid play by Fiedler and a defense that held the Patriots to 26 total yards and forced two turnovers, the Dolphins built a 16-0 halftime lead.
Fiedler was superb in the third quarter, completing eight of nine for 106 yards as the Dolphins increased the lead to 23-6.
Brady was four of seven for just 32 yards in the first half. He was sacked three times and knocked down three other times.
"We just didn't play a good first half," Brady said. "Any time you don't start fast against a team like this, the crowd is going to get into it, and it's tough to come back."
"We came out and responded," Taylor said. "This was a big game for us, for a lot of reasons. We got our butts kicked last week and came out today against the Super Bowl champs and played great. That's not the easiest task and we responded to it."
"Our entire defense was embarrassed last week to get that many yards thrown on us and not come up with any sacks," Dolphins coach Dave Wannstedt said.
Brady's fumble set up the Dolphins' first touchdown -- the eight-yard run by Fiedler. On third and goal, Fiedler escaped a pass rush by linebacker Mike Vrabel and defensive tackle Steve Martin, darted to his right and dove into the end zone with eight seconds left in the quarter.
"I knew there would be some chances to run if I found a lane through the pass rush," Fiedler said. "I went through two or three reads, but they had everything covered. I just ducked away from a defensive lineman, saw the corner out there and was able to stumble my way there."
On the Patriots' next possession, Brady threw into double coverage and Patrick Surtain intercepted the pass after it was deflected by fellow cornerback Sam Madison and returned it a yard to the New England 29.
The Dolphins were on the verge of settling for a 36-yard field goal by Mare, but an unsportsmanlike penalty on Tedy Bruschi kept the drive alive. On third and goal at the seven, Fiedler had plenty of time in the pocket and hit Chambers, who shook free of cornerback Ty Law in the end zone, giving the Patriots a 13-0 lead 3:22 into the second quarter.
"We made too many mistakes in the first half and dug ourselves a hole," Belichick said. "We turned the ball over, gave up touchdowns in the red area and didn't create enough scoring opportunities."
While the Patriots managed a total of 17 yards in their first five possessions, the Dolphins increased their advantage to 16-0 when Mare kicked a 40-yard field goal with 1:11 left in the half. Mare earlier missed a 45-yard attempt in the first quarter.
After a virtually perfect first half, Williams fumbled after being hit by Bruschi on the Dolphins' first possession of the second half and safety Victor Green recovered for the Patriots at the New England 32.
Five plays later, Patten faked Madison on an out pattern down the right sideline and caught a 34-yard touchdown with 9:35 left in the third quarter. The Patriots went for the two-point conversion and Brady failed to hit Vrabel on a tackle-eligible play in the end zone.