ARLINGTON, Texas — There are certain expectations, vast as the horizon, for the local professional football team, and when those expectations go unmet and unfulfilled — as they have for three decades and counting — another disappointing Dallas Cowboys season begets an eventful Dallas Cowboys off-season.

That is the only other phase on the sporting calendar that matters around these parts, where the team owner Jerry Jones and the thousands of fans who trudged out of AT&T Stadium on Sunday evening will, again, lament how one of the N.F.L.’s supposed injustices will go unpunished.

Asked when he had been so disappointed after a loss, Jones said, “I can’t remember.”

The Earth somehow will continue to orbit the sun as another postseason proceeds without the Cowboys, the third seed, who endured a 23-17 loss to the sixth-seeded San Francisco 49ers as predictable as it was deflating. The game’s conclusion was fittingly devastating: Time expired with Dallas, after Dak Prescott ran to the San Francisco 24-yard line, failing to run a final play.

Despite winning the N.F.C. East, sweeping their division rivals and scoring the most points in franchise history — albeit in a 17-game regular season — the Cowboys had an unsettling penchant for wilting against decent competition. San Francisco qualified as better than that. Dallas beat only one team with a winning record — the Philadelphia Eagles, who last week fielded their 11th-stringers — in the last three-and-a-half months.

“We had a team that all year would basically disappoint to some degree and then turn around and show,” Jones said. “This was a game we needed to show.”

As the 49ers advance to the divisional round next weekend at top-seeded Green Bay, which beat San Francisco on a last-second field goal in Week 3, the Cowboys will sift through the detritus of Prescott’s third loss in five career playoff games and determine just what was missing.

On Sunday, it was not one thing that doomed the Cowboys but a cavalcade of clumsiness, of critical penalties and ill-advised laterals and passes lost in the sun. One of the team’s punts, in the third quarter, hit the scoreboard. Citing how “very unusual” that was, the referee Alex Kemp called for a do-over.

If only, the Cowboys might have thought, that could have applied to the entire game. They did not convert their initial first down until they trailed, 10-0. They had 110 yards at halftime. They allowed five sacks.

When they regained possession late in the second quarter, with a chance to take the lead, a promising drive stalled in San Francisco territory on three incompletions, the third evading the hands of a diving Cedrick Wilson by mere inches.

That pass was a microcosm of Prescott’s game. Last week, with Prescott coming off a five-touchdown game at Philadelphia that buttressed the Cowboys’ confidence heading into Sunday, he asked Coach Mike McCarthy what was needed.

“I need you to keep being exactly how you are,” McCarthy replied.

Even if Prescott’s personality didn’t change as time elapsed, his passes did. They zipped high, far and wide — and, in the third quarter, into the hands of a diving K’Wuan Williams, the 49ers cornerback who intercepted another Prescott pass meant for Wilson at Dallas’s 26-yard line.

On the next play, the multidimensional receiver Deebo Samuel took a handoff, cut right and darted inside, scoring a touchdown that extended San Francisco’s lead to 23-7 with 5 minutes 50 seconds remaining in the third quarter.

“People have been trying to find the next Deebo,” Mike McDaniel, the San Francisco offensive coordinator, said last week. “The problem is there’s one Deebo.”

The Cowboys do not have him. But they do have Prescott, a set of tremendous receivers, a strong running game and an opportunistic defense that led the N.F.L. in takeaways. The Cowboys are not a complete team, but a complete team does not exist in these playoffs, and perhaps for that reason Jones reiterated in a radio interview last week that their objective “unquestionably” was to win a championship.

For an organization that identifies itself by titles, the Cowboys have not won any with Prescott, or with Tony Romo, or any other quarterback since Troy Aikman.

Of all the various and sundry subplots underpinning this matchup, none foretold the outcome quite like the power and dynamism of San Francisco’s running attack. It limited the Cowboys’ possessions. It neutralized their defensive strength, a fierce pass rush. It tormented Dallas’s eye discipline with pitches, motion and lead blockers. The 49ers scored both touchdowns on the ground and finished with 169 yards on 38 carries.

A deep red flecked the stands, with throngs of 49ers fans descending on Texas for the revival of a fierce playoff rivalry gone dormant. For so long, San Francisco and Dallas engaged in what seemed near-annual tussles for conference supremacy, though they had not convened in the postseason since January 1995.

The following season, the Cowboys edged Pittsburgh to win the Super Bowl, but they haven’t reached the conference championship game since. The 49ers have been to five over that span — and two Super Bowls, losing both, including two years ago against Kansas City, when Jimmy Garoppolo overthrew Emmanuel Sanders on a deep pass over the middle.

On Sunday, Garoppolo missed Brandon Aiyuk downfield, but otherwise his precision through three quarters enabled the 49ers to reap yardage after the catch. Garoppolo did toss an interception in the fourth quarter to Anthony Brown, with Dallas converting it into a touchdown with 8:02 remaining. But that was as close as the Cowboys got.

The chaotic regular season gave way to a postseason that, until Sunday evening, had unfurled as projected, with all three higher-seeded teams advancing. The Cowboys, yet again, are the outlier.