Miami fell into an early hole, put together only one touchdown drive and was dominated statistically by the Washington Redskins.
Landry returned a punt 69 yards for a touchdown with 10:22 left to give the Dolphins their first lead, and Miami held on for a 17-10 victory Sunday.
Landry, in his second year out of LSU, is listed behind LaMichael James on punt returns. The decision to put him back there came just before the opening kickoff.
"Was kind of a split decision," Landry said. "LaMike kind of had his hands full with kickoff return and on the offensive side of the ball also."
Cousins' two turnovers hurt, but the Redskins were right in it until the end. Unfortunately, that's nothing new.
"We battled and came up short. I guess we're all pretty tired of that around here," Cousins said. "We've done that too many times. So eventually the tables need to turn. The tide needs to be turned. And we need a day like today to end up having us be on top at the end."
Miami trailed 10-0 in the second quarter, cut it to 10-7 at halftime and pulled even with 11:34 remaining when Andrew Franks kicked a 22-yard field goal to cap a 76-yard drive.
The Dolphins then forced a punt. Landry took the ball in the center of the field and darted up the middle, dodging would-be tacklers along the way.
"The guys did a great job on their gunner, who's the best player on their special teams unit, and gave me a lot of room to make a play in," Landry said. "The rest was the other 10 guys making it happen and seeing the hole and just going."
Miami coach Joe Philbin said: "When he caught the ball there seemed to be a lot of space. He's good in the open field; he's a tough guy to get on the ground."
Washington got the ball back and drove to the Dolphins 20 before Cousins threw two straight incomplete passes.
"It's frustrating, because we did have some opportunities there, both sides of the ball," coach Jay Gruden said. "And we've got to punch it in."
And still, they lost.
"I'm not going to be down," Gruden said. "I'm upset that we lost, but I think there's a lot of good things going on."
Tannehill answered with a frenzied 80-yard drive that took less than a minute and a half, ending with a 3-yard TD pass to Rishard Matthews.
"I think the big thing was that drive before the first half," Philbin said. "We really hadn't done anything on offense in the first 27 or 28 minutes of the first half. I thought he really had good composure and made some throws on that two-minute drive."
Copyright 2015 by The Associated Press