When they go to Miami, though, they struggle.
Belichick is 4-6 on the road against the Dolphins since he became coach of the New England Patriots in 2000. Brady is 3-5.
On Monday night, they'll try to improve on those records and break a three-way tie for the division lead with Miami and the New York Jets at 2-1.
"I don't think we've played particularly well," Brady said Wednesday. "In the early part of my career, we got beat quite a bit down there. There was a long streak for a long time that we hadn't won down there.
"Then, we hit Troy (Brown) on the deep post (in 2003, a 19-13 win in overtime), then we won a few and that kind of ended it. What it means is that there's not a large margin for error down there. So as an offense, I think we have to understand that they have a very good defense and they play well at home. "
Brady has had some of his most difficult days against Miami, including a 21-0 loss in 2006 in which he completed 12 of 25 passes for 78 yards with four sacks. Last season, he threw two interceptions in the fourth quarter and Miami rallied for a 22-21 win.
"It's always tough to play down there," Belichick said. "They give you a lot to get ready for."
Since the Patriots started visiting Miami as a member of the AFL in 1966, the year the Dolphins began play as an expansion team, they are 12-33 there. At one point, the Patriots lost 16 straight games in a row to the Dolphins in Florida, finally breaking through for a 33-14 win in a playoff game in January 1986. At home and on the road, the Dolphins lead the Patriots 50-39.
New England has had its biggest problems in Miami early in the season. Belichick said that while playing in Florida then can present problems with the warm weather, it's no different than what the Dolphins have to face when they come north into the cold.
"I think you just have to make that adjustment," he said. "We've had trouble with them here. We've had trouble with them down there. They're a good football team. They give you problems wherever you play them. I think it just comes down to execution and just playing a good football game against a good team.
"Sure, it's hard down there, but it's always hard on the road. It would be hard against them no matter where we play them."
Belichick said the Patriots can't expect the Dolphins to beat themselves.
"They're a very disciplined team (with the) fewest penalties in the league," he said. "That kind of sums up the way they play. They play hard, they play tough and they make you earn everything."
Center Dan Koppen said the hot weather and noisy stadium have played a part in the team's problems in Miami, but "the main thing is they're a good football team and they play tough every week. We're expecting nothing different this week."
Brady also wants to avoid a repeat of last season's problems with Dolphins cornerbacks. The Patriots led 21-19 with a first-and-goal at the 4 with 10 minutes left, but Brady was intercepted in the end zone by rookie Vontae Davis.
"Jason Allen's in there now at corner, and he's doing a good job for them," Brady said. "And Vontae is playing really well. I'd say that. He's playing like a great corner should. He has all the physical skills and he's playing hard and he's in a good scheme for them."
Notes: About two years after the Dolphins first unveiled it against the Patriots, Belichick said he expects a good dose of Miami's wildcat offense, even though it stalled much of the time in a 31-23 loss to the New York Jets on Sunday. "I think it's still there, and every team's going to see it. Probably depending on how well you do or don't do against it." Offensive tackle Rich Ohrnberger was promoted from the practice squad to the active roster.