Ryan Tannehill threw a fourth-quarter touchdown pass and established a Miami record for most completions by a rookie quarterback, but the Dolphins suffered their third straight loss to slip further out of playoff contention.
Both teams have a 4-6 record.
The only Buffalo touchdown came just 1:30 into the game when Leodis McKelvin returned a punt 79 yards, after which Lindell made kicks of 32, 34, 42 and 19 yards.
The Bills took a 19-7 lead into the fourth quarter and then held on thanks to interceptions by Jarius Byrd and Bryan Scott.
Byrd made a diving interception at the Buffalo 35 with 2 minutes remaining and, after a punt by the Bills gave Miami a final chance, Scott picked off a Tannehill pass at the Buffalo 42 with 41 seconds to play.
Tannehill hit Davone Bess with a 2-yard scoring throw midway through the fourth period to get the Dolphins within five points. The other Miami touchdown came on a 96-yard kickoff return by Marcus Thigpen after Lindell's first field goal.
Buffalo quarterback Ryan Fitzpatrick completed 17-of-27 passes for 168 yards without an interception. Tannehill was 14-of-28 for 141 yards.