BOSTON (CBS) — The Patriots won on Sunday. They desperately needed it.

The last-second, game-winning field goal from Nick Folk gave New England a 20-17 win over the Cardinals, improving their record to 5-6 on the season. It may end up being too late to make a difference, but for the time being, the victory did boost the Patriots’ standing in the AFC playoff picture.

With the win, the Patriots climbed past the Broncos in the standings. The next slot above the Patriots is occupied by the Raiders, who lost in ugly fashion on Sunday in Atlanta. And the spot above that is occupied by the Ravens, who are scheduled to play with a COVID-ravaged roster on Tuesday. And the spot above the Ravens — the one that carries a wild-card playoff berth with it — is occupied by the Colts, who also got blown out on Sunday.

That’s the good news, technically. The bad news is that the Patriots are still in 10th place, and they still have quite a lot of ground to gain if they want to climb into a wild-card spot.

5. Cleveland Browns, 8-3
6. Miami Dolphins, 7-4
7. Indianapolis Colts, 7-4
8. Baltimore Ravens, 6-4
9. Las Vegas Raiders, 6-5
10. New England Patriots, 5-6
11. Denver Broncos, 4-7
12. Houston Texans, 4-7

In terms of a viable path to the playoffs for the Patriots, any such route would almost certainly require the Patriots winning their remaining five games to finish at 10-6. A 9-7 final record could end up being enough to sneak in, but that would require a healthy number of losses to at least three of the teams above the Patriots in the standings.

If you are looking for a reason to believe those losses may pile up for those other teams, there is some hope. Miami has a difficult schedule remaining, with a home game vs. the Chiefs and road games at the Raiders and Bills left on the docket. The Patriots have the opportunity to sweep the head-to-head if they can win in Week 15 in Miami, too.

Cleveland does have three losable games on the schedule: at Tennessee, vs. Baltimore, and vs. Pittsburgh. (The Browns’ other two games seem like sure wins, with back-to-back games against the New York teams.)

The Colts have games against the Steelers and Raiders, plus a pair of games against the Texans, who appear to be a bit of a different team now than the one that started the year. The Ravens and Raiders don’t have particularly difficult schedules remaining.

As for hope in the AFC East, that’s not entirely out of the question either, as the Bills have at least two losable games (vs. Pittsburgh, at New England) on the schedule. Any further slip-ups could bring some tie-breaking scenarios into play, provided the Patriots win out and finish at 10-6.

All of that being said … Football Outsiders calculates the Patriots’ chances of  making the playoffs at 6.4 percent. That is an increase of 2.2 percent, but it’s still a rather low number. On the flip side, the Colts’ and Raiders’ chances dipped by almost 25 percent each, so if any more major disruptions take place in the coming week or two, the numbers could change considerably.

Any more losses for the Patriots will make the picture much more bleak. But for now, as long as the Patriots keep winning games, they’ll remain alive in that busy race for a postseason spot.