ATLANTA — Many fans began leaving Mercedes-Benz Stadium before the end of Thursday night’s game, and really, who could blame them? The Falcons have burned Atlanta so many times, failing to capitalize on their promise and stomping on fans’ hopes.

So when Kirk Cousins seemed to wrap what had been an exceptional passing night against Tampa Bay by throwing a crushing interception with 1:52 remaining, well, some fans thought they knew exactly how this story was going to end.

That’s the thing about football, though — every so often, that weird ball takes a strange bounce.

Atlanta peeled off two remarkable plays — a literal last-second rush to spike the ball and set up for a field goal to force overtime, and a walk-off touchdown to maybe the unlikeliest receiver on the roster — to claim an unlikely 36-30 victory over Tampa Bay on Thursday night.

It’s one game of 17, one win of yet-to-be-determined. But it feels worth a little bit more, feels like this could be one of those pivotal victories that sets up future success. The Falcons are now 3-2, leading the division with wins over the Buccaneers (3-2) and Saints (2-2). If Cousins isn’t completely recovered from his ACL injury, well, he’s still good enough to throw for 509 yards and four touchdowns. And the team is getting contributions from up and down the roster — in the case of the final play, emphasis on “down.”

KhaDarel Hodge wasn’t drafted out of Prairie View A&M. He’s played for four teams in seven years. He has never caught more than 14 passes in an entire season. Prior to Thursday, you could count the number of his career touchdown receptions on one finger.

On the fourth play from scrimmage in overtime, Cousins found Hodge on a short 5-yard stop route that, by all normal expectations of football, should have ended with a quick tackle, setting up second-and-5 on Tampa Bay’s 40.

Instead, Hodge curled to the inside and began an all-out sprint straight at the end zone. He eluded seven different Buccaneers and ran straight toward the “C” in “FALCONS” painted in Mercedes-Benz Stadium’s west end zone. It was a remarkable, miraculous end to what had been setting up as yet another Falcon underachievement.

“When I crossed the line, I kind of blacked out,” Hodge said later. “You can’t make this up. It’s like a movie.”

His teammates swarmed Hodge, lifting him on their shoulders. He threw “A”s at the cheering crowd — two fingers down, thumb as the crossbar — as tears began filling his eyes. Once he got back on the turf, he embraced Falcons owner Arthur Blank and cry-laughed his way through on-field postgame interviews and contemplative reflections in the locker room.

“You’re fighting every year for a roster spot, fourth or fifth receiver, and just to get it out of the mud, you’ve got to wake up with that mindset,” Hodge said. “Whether it’s on special teams or whether it’s on offense, you’ve got to have that mindset and not quit, because the adversity is gonna hit, and you just got to keep going, man.”

Cousins navigated the Falcons through that overtime drive, and he also authored a frenetic, zero-margin-for-error drive to force overtime. Without a timeout, Cousins spent most of the nine-play, 51-yard drive working the sidelines. But with just 12 seconds remaining, Cousins appeared to do the one thing a team without timeouts simply cannot do in that situation — he threw to the middle, hitting Drake London for 12 yards. The Falcons raced to the line, and Cousins spiked the ball with one second left on the clock — enough time for kicker Younghoe Koo to boot through a tying field goal.

“Every single week [Cousins has] been better,” Falcons head coach Raheem Morris said after the game, “whether it’s been explosiveness, whether it’s been execution, whether it’s just a rhythm and routine with him and Zac [Robinson, Falcons offensive coordinator] and our offensive staff. I mean, it’s just getting better and better.”

These are the kind of drives that age fans, players and coaches in dog years. But on this night, with this franchise needing to keep the good momentum rolling, the Falcons will trade a few gray hairs for a necessary, thrilling victory.

It’s still way too early in the season for Atlanta to start thinking about January games. Maybe the Falcons, who can revel in this win over a bye week, will crash back to reality. Maybe they’ll lose a trap game to Carolina in Week 6, or fail to keep pace with Seattle, or fumble a Buccaneer rematch in Tampa Bay. Maybe they’ll revert to the Same Old Falcons, doing just enough to spark hope but never enough to spark joy.

Then again, maybe everything that Morris has been preaching is starting to take root. Maybe Cousins is starting to feel comfortable in the offense. Maybe the team is reducing the number of boneheaded potential game-killers from four or five times a game to one or two. Maybe all that talent Atlanta has stockpiled in the receiving corps and backfield is starting to blossom. Maybe, just maybe, this team is headed for bigger victories than moral ones.

“I don’t want to call ourselves a team of destiny,” Morris said, wisely downplaying any euphoric post-victory declarations. “There’s only one team of destiny every single year. We’ll figure that out when we get there, hopefully.”

Hey, unlikelier things have happened. Like, for instance, an undrafted journeyman outrunning an entire team for a walk-off touchdown. You never know how that football is going to bounce.