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The Patriots got their season off to the worst possible start as they went three and out and Ryan Allen's punt was blocked and recovered by the Dolphins.
New England responded immediately as Tom Brady drove them the length of the field and Shane Vereen powered through the line to go in for the two-yard score.
Brady fired his side further ahead with a touchdown pass to Rob Gronkowski, but the Dolphins pegged them back with a field goal through Caleb Sturgis. However, another field goal from Gostkowski restored the visitors' 10-point lead.
After the break, the Dolphins took advantage of ill-discipline by the Patriots to score another field goal to bring them within seven. Joe Philbin's side tied the score as Knowshon Moreno moved his side into the redzone on the ground and Tannehill found Wallace for a touchdown strike.
The Patriots failed to get anything going on offense in the second half and they paid the full price, as Sturgis added another field goal before a fourth-quarter touchdown from Moreno put the nail in the coffin.
Sturgis added another three points late on to hand the Patriots their first loss on the opening day of the season for more than a decade.