The field goal came about 3 minutes after the Cleveland's Blake Costanzo recovered a punt mishandled by the Bills' Roscoe Parrish at the Buffalo 16-yard-line.
Cundiff also booted a 24-yard field goal in the second quarter.
Jamal Lewis carried 31 times for 117 yards for the Browns (1-4).
Rian Lindell kicked a 36-yard field goal for Buffalo (1-4) in the third quarter.
Cleveland quarterback Derek Anderson completed only two passes in 17 attempts for just 23 yards, with an interception.
The Bills' Trent Edwards was16-of-31 for 152 yards and also was intercepted once.
Swim Week Miami Beach 2014 [PHOTOS]