The Rams had not scored on an opening possession of the first half or the second half this season until Monday night.
Blake Corum's 1-yard touchdown run completed a nine-play, 60-yard drive that returner Alex Bachman set up with a 32-yard kickoff return to the Los Angeles 40.
The Rams lead 14-13.
The Rams went for it on fourth-and-1 from the Buffalo 35 when Tyler Higbee was called for a false start. Higbee made up for it with a 10-yard catch on fourth-and-6.
Higbee also drew a 17-yard pass interference penalty on Cole Bishop in the end zone that set up Corum's touchdown run.
Matthew Stafford is 21-of-30 for 144 yards with a touchdown.