FOXBOROUGH — The Patriots came out of the locker room Sunday for the second half against the Dolphins looking little like the lackluster team they were in the first half.
They turned a 14-13 halftime lead into a rout in the third quarter, clinching their sixth consecutive AFC East title with a 41-13 win at Gillette Stadium.
Players donned their traditional championship hats and T-shirts in a happy postgame locker room; this year, the navy shirts said “Patriots run the East” in red block letters. Photos popped up on social media of players posing together celebrating the title, including a black-and-white picture of a smiling Chandler Jones with Tom Brady, who looks to be shouting in happiness.
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But even as excited as they were, players were overheard telling one another and team staff that the division championship was just step one, something Brady affirmed at the press conference podium.
“It’s a lot of hard work that goes into it,” Brady said. “I don’t think you ever take winning for granted; I certainly don’t, because I know how hard it is to win. I think we appreciate it, [but] I also know we have big goals every year for our team. So this is the one that is the first one to get.
“It’s great to win. It’s a great feeling. That’s why we play.”
It is the 12th division title of the Bill Belichick era; no coach has won more division crowns since the NFL/AFL merger. Belichick came into the game tied at 11 with Hall of Famer Don Shula.
The Patriots scored a franchise-record 24 third-quarter points, and scored 27 second-half points while shutting out the Dolphins, using great starting field position on two possessions to their best advantage.
Although Miami had defeated the Patriots on its field in the regular-season opener, this game proved to be another reminder that the Dolphins aren’t ready to dethrone the Patriots.
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Brady and the offense quickly established in the second half that there would not be a repeat of Week 1. The Patriots got the ball to start the third, and opened with a 34-yard pass from Brady (21 of 35, 287 yards, 2 touchdowns, 1 interception) to Rob Gronkowski.
Later, facing third and 11, Brady dropped back, scanned the field, pump-faked, and took off running, not stopping until he was knocked out of bounds 17 yards later by Dolphins safety Walt Aikens. It was Brady’s longest run since 2007.
Brady said he was “pissed off” during the play, which is why he didn’t slide.
“I could have slid, but I wasn’t in the best mood at that time,” he said. “If he was a bigger guy, I would have thought really hard about sliding, but once I was in the secondary, things happen pretty quick for me out there.”
Many of Brady’s teammates had comments — and jokes — about the run, such as Brandon LaFell: “It was in slow motion, but it was good.”
LeGarrette Blount scored immediately after Brady’s run, crossing the goal line from 3 yards out.
Miami opened the second half with a punt, and the Patriots increased their lead to 24-13 with a Stephen Gostkowski field goal. It made Gostkowski the franchise’s all-time leader in scoring, passing Adam Vinatieri.
Two plays, in rapid succession, effectively put the game out of reach. Miami’s Ryan Tannehill was picked off on first down as Patrick Chung pulled in a ball intended for running back Lamar Miller that he had batted up in the air. One snap later, Brady hit Gronkowski down the left seam for a 27-yard touchdown that put the Patriots ahead, 31-13.
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Then a short Brandon Fields punt combined with a 13-yard Danny Amendola return gave the Patriots good field position once again, and they turned it into a touchdown, Brady with a perfect floater to Julian Edelman for a 6-yard score.
“Give it up to them for outplaying us in the first half,” Patriots guard Ryan Wendell said. “We played so bad as an offensive unit, as an offensive line, myself as an individual, that we had nowhere to go but up [in the second half].
“There are three phases to the game. The defense was doing its job, special teams was holding up its end, we weren’t doing our job.”
Miami picked up 50 yards on its first snap of the game, a pass from Tannehill (29 for 47, 346 yards, 1 touchdown, 2 interceptions) to receiver Mike Wallace, who was covered by undrafted rookie Malcolm Butler. But a few plays later, on third and 6, the Dolphins ran the ball when logic dictated pass, and Miller was stopped well short of the first-down marker.
Dolphins kicker Caleb Sturgis lined up for a 41-yard field goal try, but it was blocked by Jamie Collins. Kyle Arrington scooped up the loose ball and returned it 62 yards for his second career touchdown to give the Patriots a 7-0 lead.
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“That’s kind of what the outside guys are looking for,” Belichick said. “They’re looking for a block to put themselves in a position, which [Arrington] did, to be able to attack the ball.
“Kyle is a fast guy. Once he got a little bit of space, I don’t think there are too many guys who can run him down. It was good — he did his job. He was in position and took advantage of the opportunity and turned it into points.”
Arrington suffered a leg injury later in the first half and did not return. The veteran cornerback has never missed a game in his career.
Though the Patriots had the early 7-0 lead, the offense did little to build on it, with Brady getting intercepted on his fourth pass attempt of the afternoon. Dolphins linebacker Jason Trusnik got a hand on the pass, deflected it in the air and came down with it.
Brady had three passes batted at the line of scrimmage, all in the first half.
Miami was able to get 3 points off the turnover.
The Patriots’ second touchdown came thanks to the defense, as safety Duron Harmon intercepted a Tannehill pass intended for rookie Jarvis Landry. The pass was too high for Landry, and Harmon came close to a pick-6, but was pushed out of bounds at the 8.
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Shane Vereen ran the ball in from the 3, taking advantage of a big hole because Rob Gronkowski drew two defenders.
The Patriots had just 102 yards of offense in the first half; they had 195 in the third quarter alone.
Miami put another field goal on the board, then scored a quick touchdown at the end of the first half after a review showed Wallace did come down inbounds on a one-handed, 32-yard catch.
More coverage:
■ Patriots 41, Dolphins 13: Patriots capture AFC East title again
■ Shaughnessy: Winning AFC East only the beginning
■ On football: Brady’s scramble picked up Patriots
■ Harmon, Patriots defense kept Dolphins at bay
■ Notebook: Chandler Jones plays like he never left
■ Special teams play big role in win over Dolphins
■ Opposing view: Same old losing script for Dolphins
■ Belichick, Patriots adjusted at halftime, and the rout was on
■ Tailgating: Fans add wood-fired pizza oven to party
■ Patriots fan wins $1 million at halftime by picking No. 12
Shalise Manza Young can be reached at syoung@globe.com. Follow her on Twitter @shalisemyoung.