LAS VEGAS — The running joke on social media last week was that if the circumstances called for it, the Raiders and the Chargers should make a pact.

If the Colts lost to the lowly Jaguars, which they did Sunday, both Los Angeles and Las Vegas could mathematically enter the postseason with a tie. That meant Sunday night’s prime time game could theoretically have featured three hours of Justin Herbert and Derek Carr kneeling the ball to produce a stalemate.

Instead, the conclusion of the N.F.L.’s longest regular season was a competitive overtime affair, that saw both franchises determined to end the other’s season. The Raiders finally prevailed, 35-32, in overtime, gaining the A.F.C.’s final playoff berth only after thwarting the Chargers rally from a 15-point deficit in the fourth quarter of regulation.

It was a fitting end to the final game of the first regular season to feature 17 games, a campaign that bloated the schedule with meaningless games early Sunday and ended with two teams determined that their matchup would not be one of them.

“I think we all respect the game and the N.F.L. shield and the integrity of this game far too much to be complicit in something like that,” Chargers Coach Brandon Staley said earlier in the week.

After pulling to within a score late in the fourth quarter, the Chargers’ Pro-Bowl quarterback, Justin Herbert, masterfully drove the offense 83-yards in the final two minutes of regulation, pitching a 12-yard strike to Mike Williams to knot the score at 29-29 and send the game into an overtime, prompting the curious question of how an impasse would affect the rest of the playoff landscape.

The immediate beneficiary of the Colts loss, the Pittsburgh Steelers, would have had their No. 7 cruelly snatched back had the Chargers and Raiders’ impasse persisted. And the sports betting markets, newly legalized in many states, would have gotten a jolt.

Both teams traded overtime field goals, with the Raiders regaining possession after the Chargers’ Dustin Hopkins converted his 41-yard kick with 4:30 left and the score tied at 32.

Led by hard, slashing running from Josh Jacobs, who posted 132 yards and a touchdown, Las Vegas drove 46 yards into field-goal range. In that sequence, Jacobs rushed for a 7-yard gain, and the Chargers called a time out, stopping the clock, to substitute a personnel package. Before that moment, interim coach Rich Bisaccia said the Raiders contemplated letting the clock drain to finish with a tie, but the timeout changed their approach.

“We were certainly talking about it on the sideline Bisaccia said.

On third-and-4 from the Chargers’ 39-yard line, Jacobs rushed for 10 yards setting up a Daniel Carlson 47-yard, walk-off field goal. As the ball sailed through the uprights, Raiders defensive end Maxx Crosby threw his helmet and ran onto the field in excitement. Carr, who threw for 186 yards and two touchdowns, later pumped his hands as he walked off the field and hurled a game ball into the crowd.

The Raiders’ win gives them a coveted slot in the postseason, faced with a road matchup against the No. 4-seed Cincinnati Bengals. But Las Vegas’s persistence, winning their final four games to advance to the postseason under an interim coach and with a shell of its season-opening roster, exemplified the possibility offered by a stretched out schedule.

The 2021 season was again dogged by Covid-19-related player absences, which resulted in cobbled together lineups and unexpected losses, and many of the league’s juggernauts — Patrick Mahomes’s flashy Kansas City offense, the Dallas Cowboys — suffered swoons that stretched out to imperil their standings. The added game gave those playoff-bound high seeds the opportunity to revert to form, perhaps none so much as the Raiders, who as late as mid-December were under .500.

“Every single week you got to be ready to go to be at your best” said Crosby, who finished with six tackles and two sacks. His white arm sleave and white pants were plastered with green grass stains from Allegiant Stadium’s surface. “I love it, there’s nothing else I would want.”

The playoff berth had seemed unlikely for the Raiders, who have been roiled by calamity this season. The team’s head coach, Jon Gruden, resigned in October after The New York Times and Wall Street Journal reported on racist and homophobic emails he sent from 2011 to 2018, when has an ESPN analyst. Weeks later, the team released Henry Ruggs III, a first-round draft pick in 2020, after the receiver crashed his sports car into the vehicle of Tina Tintor, 23, killing her when her car burst into flames. He was charged with two felony counts of driving under the influence and two felony counts of reckless driving.

The team also released another 2020 draft pick, cornerback Damon Arnette, in November after he brandished a gun on social media and threatened to kill someone. Nate Hobbs, a cornerback, was also charged with driving under the influence, a misdemeanor, last week after he fell asleep in his vehicle at a parking garage.

The rapid succession of incidents raised outside amplified the Raiders’ football struggles. Limping to a 3-5 record in Bisaccia’s first eight games left long odds for the Las Vegas team, but three wins in games decided by one score — sloppy outings against the Covid-ravaged Browns, the Colts and the Broncos — lifted them into the race.

“We locked the doors every day on Monday, and the people that were inside that building didn’t stop believing and it showed todayCarr said.

That preparation and resolve was evident in the first half, when the Raiders looked sharp and the Chargers seemed hesitant. Las Vegas burst to a 10-0 lead before Los Angeles eventually settled and scored 14 unanswered points at the start of the second quarter.

On the Raiders’ ensuing possession, the Chargers’ defense forced third-and-23 at the Las Vegas 35-yard line, but the unit, which has been notoriously porous against the run, allowed Jalen Richard to slither up the middle untouched for 23 yards, creating a fresh set of downs.

The Chargers forfeited 108 yards on 10 penalties no Sunday, none more important than when referees flagged defensive back Chris Harris Jr. for pass interference in the end zone two plays after Richard’s run. The Raiders scored a touchdown on the next play, increasing their lead to 17-14, and they never trailed the rest of the night.

The Raiders had not been to the playoffs since 2016 and have not won a Super Bowl since 2002. For Bisaccia, it is a bullet point on his résumé, should the team’s owner, Mark Davis, interview him to permanently remain as coach.

That optimism was not felt by the Chargers, who brought in first-year head coach Brandon Staley for his aggressive, analytic approach, which resulted in two more wins than in 2020. The boon of a 17th game, was a net loss for Los Angeles, which had been favored Sunday.

“We just couldn’t create enough separation,” Staley said. “We had to have this game and we just couldn’t quite finish it out.”