The Patriots entered the game needing one first down to establish an NFL record, since they were tied with the 2011 Saints at 416. It didn’t take long, with Brady connecting with Aaron Hernandez on a 14-yard pass on the game’s first play . . . Steve Gregory’s first-quarter interception meant that the Patriots forced at least one turnover in all 16 games, the first team since the 2010 Falcons to accomplish the feat. The Patriots have at least one takeaway in 27 straight games . . . Receiver Kamar Aiken was promoted to the 53-man roster Saturday, but was one of seven players on the inactive list come Sunday. Joining Aiken was cornerback Alfonzo Dennard, who missed his second straight game with hamstring and knee injuries; offensive linemen Markus Zusevics and Nick McDonald; defensive lineman Jake Bequette; and defensive backs Nate Ebner and Marquice Cole, who injured a finger in the win at Jacksonville . . . The Dolphins were shut out in the first half for the first time in 32 games, which had been the second-longest active streak . . . Backup quarterback Ryan Mallett was the up-man on a fourth-and-1 play from midfield, with punter Zoltan Mesko behind him. The unusual personnel forced the Dolphins to take their first timeout of the second half. When play resumed, Mallett was back on the sideline and Mesko punted. Mallett was one of two Patriots who didn’t play, joining Talib . . . Dolphins running back Reggie Bush needed just 40 yards to record the second 1,000-yard season of his career, but he was limited to 26 yards on eight carries . . . Stephen Gostkowski’s four extra points gave him 153 points on the season, the second-highest total in team history. Cappelletti had 155 in 1964.