Landry bounced back from a potentially disastrous fumble, and the Dolphins ended a streak of three consecutive losses to Buffalo, overcoming a third-quarter deficit to win 22-9.
Ryan Tannehill shook off five sacks to throw late touchdown passes of 7 yards to Brandon Gibson and 8 yards to Landry. Tannehill went 26 for 34 for 240 yards, and Lamar Miller rushed for 86 yards.
Miami trailed 9-3 before outscoring Buffalo 19-0 over the final 18 minutes. The Dolphins improved to 6-4, their best record after 10 games since 2008.
The Bills, trying to end a 14-year playoff drought, fell to 5-5 with their second loss in a row.
Stymied by Buffalo's front four in recent meetings, the Dolphins had scored one touchdown in 33 possessions against the Bills before late TD drives of 80 and 63 yards. Otherwise a stout defence did the heavy lifting for Miami, which scored a safety on a penalty.
The Bills, ranked last in the NFL in red-zone touchdown efficiency, mounted grinding drives of 67 and 85 yards on their first two possessions. But Miami held them to a field goal each time, and those were their best TD chances.
The Bills have reached the end zone once in their past nine red-zone trips.
With the Dolphins leading 12-9, Landry lost a fumble on a kick return, but their defence again dug in, and former Miami kicker Dan Carpenter missed a 47-yard field goal try. He made earlier attempts of 33, 21 and 46 yards.
The Dolphins, also ranked poorly in red-zone efficiency, missed chances early themselves. They came away with three points from trips inside the 20 on their first two possessions, and didn't reach the end zone until 42 minutes into the game.
Miami led 10-9 before scoring a safety when Kyle Orton was flagged for intentional grounding from the end zone. Under pressure from Olivier Vernon, Orton threw a pass that landed closer to the Bills sideline than to any player.
The Bills padded their NFL-leading sack total while working against Miami's makeshift line, reshuffled after left tackle Branden Albert's season-ending knee injury last week. But Tannehill kept getting back up, and he finished with a passer rating of 114.8.
Orton's rating was 69.7. He went 22 for 39 for 193 yards, and the Bills — missing their top two running backs — netted only 54 yards on the ground.