Yes, this is really happening: The Red Sox are headed to the American League Championship Series

Red Sox players mob Kiké Hernández, whose walkoff sacrifice fly ended Game 4 and sent them to the AL Championship Series.Stan Grossfeld/Globe Staff

How to explain it? How can all of this be happening for a Red Sox team that finished in last place a year ago, whose best-case scenario for 2021 seemed like respectability, whose season seemed ready to unravel time and again over a two-month stagger to the finish line of the regular season?

Stop asking. No need to wonder — not now. Simply accept that this once-incredible proposition has come to life: The Red Sox will be one of the four last teams standing in baseball this year, having secured a berth in the American League Championship Series by dispatching the Rays, 6-5, in Game 4 of the AL Division Series.

“We always said we had a good baseball team that had some holes, and we still have some holes, but at the end, for how bad it looked sometimes, we’re still here,” beamed manager Alex Cora. “We’re still in the dance. We’re still in the tournament. And we’re moving on to the ALCS.”

The victory proved as unsteady as most of the season that has preceded it, with the Red Sox forging an early 5-0 lead but then springing a steady leak that yielded a 5-5 tie in the eighth. But after five listless innings, the team found a final burst across the finish line on Marathon Monday, when a ninth-inning sacrifice fly by Kiké Hernández scored pinch runner Danny Santana to secure the series-clinching victory and inspire bedlam among the 38,477 wired Fenway patrons.

With their victory, the Red Sox sent home Tampa Bay — last year’s AL pennant winner and possessors of the best regular-season record in the American League this year — with a tension-filled 3-1 triumph in the best-of-five ALDS. They’ll face the Astros or White Sox on the road in Game 1 of the ALCS on Friday.

Christian Vázquez initiated the winning rally with a leadoff single in the ninth. He advanced to second on a Christian Arroyo sacrifice bunt, then reached third when pinch hitter Travis Shaw dribbled an infield single to third. Hernández lined an 0 and 1 fastball from J.P. Feyereisen to left, plenty deep enough to score Santana, a victory that proved far more difficult to secure than seemed likely six innings earlier.

Rays rookie Shane McClanahan — who logged five shutout innings as the Game 1 starter — entered a scoreless game in the bottom of the third. The Sox, unable to do anything against him in the series opener, did not have the same issue in Game 4.

With two on and two out, Rafael Devers dug in against the hard-throwing lefty. In the first game of the series, McClanahan left Devers wincing, blowing 100 m.p.h. heat at the top of the zone past the injured Red Sox slugger. This time, Devers was ready when McClanahan offered a 98 m.p.h. heater down the middle.

Devers obliterated the pitch, launching the ball for a photo-op against the night sky before it paused to build suspense before its descent. When the orb re-entered the atmosphere, it crashed into the first row of the bleachers in straightaway center field, a three-run homer that left both Fenway and McClanahan shaking.

“I make the adjustments when I need to. That’s what I did today,” Devers (3 for 4) said through a translator. “I knew I hit it pretty good. I was hoping it would go out . . . It was very emotional.”

Rafael Devers' three-run homer in the third inning Monday night provided a boost to the Boston offense.Matthew J Lee/Globe staff

The Sox kept pushing. Xander Bogaerts singled and scored on an Alex Verdugo double off the Wall. J.D. Martinez likewise pelted the Monster on a full-count slider for a single to score Verdugo and make it a 5-0 game. McClanahan departed following a five-run eruption that was matched in magnitude by a full-tilt Fenway throng that was ready to celebrate.

“Pretty devastating,” Rays manager Kevin Cash said of the hole.

In contrast to McClanahan, Eduardo Rodriguez faceplanted in Game 1 but dominated in Game 4. The Sox veteran opened the game with three perfect innings, striking out five of the first seven batters.

The last of those strikeouts proved the most impressive, with the pitcher locking horns with Austin Meadows for an astonishing 17 pitches — the longest postseason at-bat in the Baseball-Reference.com database — before finishing him with a slider.

Armed with his five-run lead, Rodriguez — pitching on three days’ rest following his 1⅔-inning start in Game 1 of the ALDS — gave up his first baserunner to open the fourth (a Randy Arozarena single) but retired the next three hitters.

Still, the Rays’ tenacity is well-known, and so it proved unsurprising when they started to whittle the deficit. A Jordan Luplow leadoff double in the fifth resulted in Tampa Bay’s first run, making it a 5-1 game.

Rodriguez briefly returned to the mound in the sixth, but Kevin Kiermaier’s bloop double down the left field line ended his night. As Cora made his way to the mound, Vázquez hugged his pitcher, who received a sustained ovation as he made his way to the dugout.

“Today was really special for me,” Rodriguez said. “It was just amazing to go out there and have the opportunity to do what I did today.”

Eduardo Rodriguez allowed two runs in five innings of work.Barry Chin/Globe Staff

But the atmosphere of celebration was tempered when reliever Tanner Houck gave up a one-out, two-run homer to dead center by Rays marvel Wander Franco. The switch hitter’s second homer of the series brought the Rays to within 5-3 and put Franco in exceptional company, as he joined Miguel Cabrera, Juan Soto, Andruw Jones, Mickey Mantle, and Devers as the only players ever with multiple playoff homers before turning 21.

Though Houck escaped the inning without further harm, Fenway festivity transformed into anxiety, a two-run lead through six innings against the Rays representing a decidedly uncertain proposition. Forming dread came to fruition in the eighth.

The Rays — the best late-inning offense in baseball — remained true to their rallying form. They jumped on Ryan Brasier — who had made 11 straight scoreless appearances entering Monday – with three straight hits, all off fastballs: A leadoff double from Mike Zunino, an RBI double by Kiermaier, and finally, a game-tying RBI single rifled through the right side of the infield by Randy Arozarena.

“We clawed back in it,” Cash said.

Kike Hernandez gets a ride from his teammates after delivering the game-winner Monday night.Matthew J Lee/Globe staff

But Garrett Whitlock entered in relief of Brasier and stabilized the game, stranding Arozarena with three quick outs in the eighth. He returned for a perfect ninth that set the stage for the Sox to walk off in the ninth and advance to the ALCS for the 12th time in franchise history — with perhaps their most unlikely of their seven teams to reach this point in the 21st century.

“Here we are surprising everyone but ourselves,” Hernández said. “We knew in spring training that we had the team to make it this far, and here we are.”