They now lead the NFC East after avoiding an 0-2 start, and overcoming a 19-point second-half deficit could certainly have a galvanizing impact on a team that had been crushed by injuries and plagued by underwhelming performances on both sides of the ball six quarters into the 2020 NFL season.
But at times like these, following moments like those, it's easy to lose sight of the problems that forced a team to rely on a football miracle for a victory.
If multiple Falcons players hadn't inexplicably stood and stared at the rotating ball generated by a late Dallas onside kick that was astonishingly and awkwardly recovered by the Cowboys, many fans and pundits would be writing the Cowboys' eulogy right now.
We'd be highlighting the three lost fumbles that told the story of an embarrassing first half, and we'd be wondering if they're simply too depleted to compete.
They're without Tyron Smith, La'el Collins and Cam Erving along an offensive line that already lost star center Travis Frederick to retirement this offseason, tight end Blake Jarwin suffered a season-ending knee injury last week, and a defense that lost top cornerback Byron Jones in free agency hasn't been right without injured linebackers Leighton Vander Esch and Sean Lee and starting corner Anthony Brown.
Reality check: That defense allowed points eight times in a nine-drive span Sunday. It has a total of two sacks in two games against teams with vulnerable offensive lines and has already allowed 17 third-down conversions on 34 attempts (plus three fourth-down conversions on as many attempts). That unit has one takeaway thus far against opponents that committed a combined 49 turnovers in 2019.
The Cowboys allowed the Los Angeles Rams and Falcons to completely control them during the first six quarters this season, and they benefited significantly from Atlanta's second-half gaffes in Week 2.
The onside-kick recovery attempt was just comical, but the Falcons also failed to put the game to bed when Julio Jones dropped a potential touchdown in the third quarter. Atlanta sheepishly elected to punt following that 3rd-and-2 failure at the Dallas 41-yard line, and the Cowboys took advantage with a touchdown drive in response.
The Falcons also settled for two field goals inside the Dallas 10-yard line, and head coach Dan Quinn got caught overthinking with a failed first-half two-point conversion attempt in a 26-7 game. Beyond that, the Cowboys also likely benefited from the fact Atlanta lost starters Kaleb McGary, Ricardo Allen and Takk McKinley to midgame injuries.
The model for this victory isn't just unsustainable; it's realistically unreplicable.
And now, a Cowboys squad that is just 3-5 in its last eight games has to go on the road to face a Super Bowl contender in the Seattle Seahawks before hosting the unpredictable-but-talented Cleveland Browns. They also draw the thus-far-impressive Arizona Cardinals and the mighty Pittsburgh Steelers ahead of their Week 10 bye.
They might be able to play the way they did during the first game-and-a-half of the 2020 season during that stretch and remain in playoff contention, but that'd just be because the Philadelphia Eagles, New York Giants and Washington Football Team don't look any more competent early this season.
Eventually, highly paid star running back Ezekiel Elliott will need to be a game-changer, the offense will have to become more reliable as a whole, and the defense will have to generate far more pressure. They'll need to start games faster (a problem that existed prior to this season and apparently hasn't vanished under new head coach Mike McCarthy), and the play-calling will need to become better on both offense and defense.
And while they can't be blamed for the hand dealt by the Football Gods thus far, they'll have to do a better job coping with key injuries.
In a weak division with a seven-team playoff field, the Cowboys aren't likely to fade from relevance. And this comeback win certainly helps their cause. But if they don't learn from the mistakes that forced them to rely on an opponent's miscues in order to avoid an 0-2 start, and if they don't truly rally based on Sunday's climactic finish, a Dallas team loaded with flaws and weak spots won't be a serious contender.
Brad Gagnon has covered the NFL for Bleacher Report since 2012. Follow him on Twitter: @Brad_Gagnon.