The win gives the Rams an even record (6-6-1) on the season. More importantly, the team's three-game winning streak keeps the Rams in the NFC playoff picture.
Let's take a look at the Rams' postgame grades and evaluations.
Final Score: Rams 15, Bills 12
Overall Grade: D
Despite the win, Sam Bradford had a dreadful day at the office Sunday afternoon.
He was inefficient, inaccurrate and often inept with the ball.
Bradford finished the game 19-of-29 for 209 yards. He threw one touchdown, albeit the game winner, and one interception for a passer rating of 62.9.
Too many times Bradford missed his receivers. On more than one occasion, those receivers bailed Bradford out by reaching back to make difficult catches.
Bradford was unable to connect on any deep balls, but that was not all his fault, as Chris Givens dropped a teardrop pass laid perfectly on his arms.
Quarterbacks get the glory when the team wins, and Bradford deserves all the credit for leading the offense down the field for the winning touchdown.
For 55 minutes, Bradford was dreadful. But for the final five, he showed he still can be a leader for this team.
Overall Grade: C-
Jackson had a tough day running the ball. He gained only 64 yards on 19 carries (3.4 average).
He did get into the end zone, scoring on a one-yard run in the third quarter, but Jackson time and again found himself running directly into a wall of Buffalo defenders.
In the end, the committment to the running game paid off.
The Rams were behind by almost seven minutes in time of possession at the half, but they caught up in the second half to nearly get even with the Bills.
Jackson did what he had to do in this game. It was not pretty, but it was mistake free.
Overall Grade: D+
Brandon Gibson has made a lot of big catches this season. Not one was bigger than the game-winning score in the final minute against the Bills.
Gibson saved the Rams' season (at least for one more week) and kept the team in the NFC playoff hunt. He finished the day with a team-high six catches for 100 yards and the touchdown.
For the rest of the receiving crew, it was a pretty ugly performance. There were a fair share of drops, including multiple by Chris Givens.
Givens, in fact, hauled in just three catches on 10 targets. Although, he did get open to snag the two-point attempt that increased the Rams' lead to three points at the end.
Austin Pettis caught all five passes thrown his way, netting 33 yards, but he made a terrible error in the fourth quarter by going down before the first-down line.
Brian Quick was again his usual ghostly self, catching only one pass.
The absence of Danny Amendola is clearly evident among this group. If anyone says that Amendola's injuries hurt his chances, just put in this game tape and you will see how valuable he is to this team.
Overall Grade: A
The Bills came into this week's game ranked fourth overall in rushing yards, averaging 5.2 yards per rush attempt.
The Rams held the C.J. Spiller-Fred Jackson combo to just 51 combined yards on 16 carries (3.2 average), and Jackson lost a fumble deep in Rams territory that probably cost the Bills the points they needed to win the game.
The Rams front four recorded all four of the team's sacks on Ryan Fitzpatrick, with everyone getting a piece of the action.
Michael Brockers led the way with 1.5 sacks. Robert Quinn also netted a sack to go with two tackles for loss.
The Rams hit Fitzpatrick 11 times and were solid the entire game, and there were no lapses by the defense.
They were the reason the Rams still had a shot to win in the final minute, despite having only seven points on the scoreboard before the 60th minute of the game.
Overall Grade: A-
Buffalo was able to move the ball in the passing game, as Fitzpatrick completed 25-of-32 passes. But the Bills only gained 242 yards through the air and only found the end zone one time.
The Rams secondary held the Bills to just 3-for-12 on third down and committed just two penalties the entire game.
It was a bend-but-don't-break kind of game for the Rams' DBs. No Buffalo wide receiver reached 100 yards, with the closest being 71.
Scott Chandler found a lot of space in the middle of the defense, but that's been the case for many tight ends against the Rams defense.
Stevie Johnson was mostly held in check, with a team-high six catches. He had one nice grab that accounted for over half of his receiving yards.
There were no turnovers by the Rams DBs, but there were also very few mistakes.
Considering the Rams run defense was nearly perfect, it was just as impressive to see the pass defense do its job.
Overall Grade: B
It was a quiet day for the Rams special teams.
Greg Zuerlein made only one appearance on a scoring play, kicking an extra point after the Jackson touchdown run.
Johnny Hekker was the workhorse for the crew, punting eight times.
Hekker had several nice punts, pinning the Bills inside the 20 twice. Hekker's game-saving moment was at the top of the fourth quarter. A bad snap sailed over Hekker's head.
However, a touchdown was saved when Hekker scooped up the ball and in one motion shot a quick punt over the defense. The 48 yards that ball sailed were possibly the biggest of the day.
Chris Givens and Austin Pettis held their own in the return game. Pettis found some running room on two punt returns, averaging nearly 12 yards on both of his attempts.
The Bills have some explosive kick returners; however, Brad Smith and Leodis McKelvin were kept away from big plays.
The Rams special teams was never called on to win the game, but it certainly did its part to not lose the game, for whatever that's worth.
Overall Grade: C+
Anytime a team can win on the road, the coaching staff deserves credit. It wasn't a pretty performance, but the Rams were excellent on defense and did just enough on offense to pull out the victory.
In the first half, the tenacity of the Rams defense was surpassed only by the offense's ineptitude.
As the most penalized team in the NFL, it is worth mentioning that the Rams did not get flagged for a penalty until midway through the second quarter.
Credit the coaching staff for making some adjustments on offense in the second half. Sam Bradford found a rhythm with Brandon Gibson and the Rams converted three first downs on the half's opening drive.
After a couple emotional wins and week's worth of talk about the playoffs, it was natural to think the Rams might come out a little flat.
Traveling to Buffalo, dealing with the weather and not having Danny Amendola, Jeff Fisher had his hands full.
To Fisher's credit, the team came out with a lot of energy, particularly on the defensive end. The team threw a lot of blitzes at the Buffalo offense and got enough pressure on Fitzpatrick to keep him from doing real damage.