Brady threw for only 153 yards, and Randy Moss was held without a catch for the first time since 2006, but the Patriots still registered their biggest point total yet. They're averaging 33 points per game.
New England trailed 7-6 at halftime, but when Brandon Tate returned the second half kickoff 103 yards for a score, the deluge was on before a stunned crowd. In the fourth quarter, the stadium quickly emptied.
"Where's everyone going? 'The party' is just getting started at Sun Life Stadium," the Patriots posted on their Twitter feed.
"We had a tidal wave hit us," Dolphins coach Tony Sparano said. "It was a mess. Embarrassing. These fans deserve better than this."
New England (3-1) moved into a tie with the New York Jets for first place in the AFC East, while the Dolphins (2-2) dropped to third place with their second divisional loss at home in eight days.
Chung blocked a punt to set up a touchdown, then blocked a field goal that Kyle Arrington returned 35 yards for a score.
"We practiced everything that happened -- all of those blocks, and people doing their job allowed me to make a play," Chung said.
He returned an interception 51 yards for New England's final score.
Another unexpected contribution came from linebacker Rob Ninkovich, who had the first two interceptions of his five-year career. Chung and Arrington scored their first career TDs, and Patriots reserve fullback Danny Woodhead scored on an 11-yard reception.
The Patriots totaled 17 points in a span of 2:16 bridging halftime to take command.
Miami's Chad Henne was 29 of 39 for 302 yards and two scores, but he was yanked with 6 1/2 minutes left after tying a career high with his third interception.
Henne blamed his first turnover on a forced pass, the second on inaccuracy and the last on a miscommunication.
"Overall it's my fault," he said. "I'll take that one as a quarterback. I'll put that on my shoulders."
The pass picked off by Chung was especially ugly.
"It shocked me," he said. "I was like, 'He threw it? Thanks.'"
Tyler Thigpen finished up and threw the Dolphins' fourth interception.
The Dolphins lost even though they netted 400 yards and had 23 first downs. Ninkovich's picks set up two field goals, and New England held Ronnie Brown to 27 yards rushing.
The Dolphins had a punt blocked for the second week in a row.
Tate took the second-half kickoff in the end zone, cut toward the right sideline and scored untouched, giving the Patriots their first lead. Miami went three and out, and Chung blocked Brandon Fields' punt.
"It's not the guy who blocks it, it's the other guys that hit the gaps and take the blockers and open it up for the guy that they missed," Patriots coach Bill Belichick said. "It was a nice job by the whole team. ... We've been close on a couple and haven't gotten them, so it was great to get them."
Two plays later, BenJarvus Green-Ellis scored on a 12-yard run.
When the Dolphins lined up for a 53-yard field goal attempt that would have cut the deficit to 10 points, Chung again broke through to block the kick, and Arrington recovered with nothing but the end zone in front of him.
"I was just fortunate enough to be in the right place at the right time," Arrington said.
"Special teams decided this game," said Dolphins kick returner Nolan Carroll, who also plays on the coverage team. "It's a blow to our gut."
As a result, the Patriots didn't need Moss. He was targeted only once, when he stretched for a pass in the end zone, but the ball deflected off his hands and New England settled for a field goal.
"If they're taking one guy away, everyone else has to come out and play well," Patriots receiver Wes Welker said. "It's a team effort, and that's exactly what today was."
Brady was sacked three times but finished 19 of 24 with no interceptions.
Tate had a 97-yard kickoff return for a score in the season opener against Cincinnati. ... Moss, covered by Vontae Davis most of the game, was shut out for the first time since Nov. 19, 2006, against Kansas City. ... Patriots LB Jerod Mayo had 16 tackles.
Le'Veon Bell scored on a 1-yard wildcat run as time expired to give Mike Vick and the Pittsburgh Steelers a stunning 24-20 victory over the San Diego Chargers on Monday night.
The NFL would have had another wild controversy on its hands, had Le'Veon Bell not scored on the final play from scrimmage to give Pittsburgh a win Monday at San Diego.
An MRI has confirmed what the Kansas City Chiefs feared during Sunday's game: Running back Jamaal Charles has torn the ACL in his right knee and will miss the remainder of the season.
Chargers tight end Antonio Gates became the ninth player in NFL history to catch 100 touchdowns with a 12-yard reception in the first quarter of Monday's 24-20 loss to the Steelers.
Former USC coach Pete Carroll said Monday that he's saddened by Steve Sarkisian's situation and he has reached out to his former assistant.
Twitter accounts for the websites Deadspin and SB Nation were suspended by the social media platform Monday night, after the NFL filed notices related to use of copyrighted video highlights.