This time, he got a win as well.
Moreno now has 358 yards on the ground in his last two regular-season games against New England, the first of those being a 224-yard effort in Denver's loss at the Patriots last season.
That one, Moreno said he barely remembered. This one, he'll surely savor.
Tannehill completed 18 of 32 passes for 178 yards.
"They just played better," Gronkowski said. "They've got a good team. They've got a good defense."
The Patriots had a 10-point lead at the half, which usually means a Patriot win. New England had prevailed in 16 of its last 17 games where it held a double-digit edge at intermission.
But on Sunday, an 89-degree day that felt like 99 degrees when factoring in the humidity, New England wilted.
Helped by a roughing-the-passer penalty early in the drive and a pair of third-down completions by Tannehill as it went along, the Dolphins went 85 yards in about 6 minutes to put the game away. Moreno barged in from the 4 with 3:36 remaining to push the lead to 30-20, and the outcome was mostly academic from there.
"Once he has the ball in his hands," Tannehill said, "he's going downhill."
The Dolphins blocked a punt on the game's first possession, then took advantage of the short field with Tannehill connecting with Miller for a 4-yard touchdown. It marked the first time since 1992 - when a couple of guys named Dan Marino and Mark Duper hooked up for the honors - that Miami's initial offensive sequence of a season ended with a passing touchdown.
Wallace fumbled away a catch, Tannehill was intercepted trying to find Wallace with a deep ball, setting up a possession where Brady found Gronkowski for a score. And that was followed by Miami's Lamar Miller - on a run where he would have gotten a first down - getting flipped over on a play where both one of his shoes and the football went flying.
It was 20-10 at the half, New England outgaining the Dolphins 248-138 to that point. And then everything changed.
NOTES: Brady passed Warren Moon for No. 6 on the all-time NFL passing list, and could eclipse the 50,000-yard career mark later this month. ... Miami lost starting LBs Danell Ellerbee (hip) and Koa Misi (ankle) in the first half, neither returning. And those injuries came with another would-be starter in Phillip Wheeler already out. ... Dolphins DE Cameron Wake has had at least one sack in each of New England's last five trips to Miami. ... The Dolphins didn't punt in the first three quarters, then punted twice in the first 3:58 of the fourth.
Copyright 2014 by The Associated Press