The last time the Red Sox made an improbable run from having finished last the season before to the top of the world, they also had to go through the Rays in a division series. They won that one in four games, the same as they did Monday night. The score in Game 4 was 3-1 for Boston eight years ago. Two of those runs were scored by a kid named Xander Bogaerts, who came into the game as a pinch-hitter and finished it at shortstop, where he has remained ever since for the Boston Red Sox.

It is Bogaerts, at 29 still one of the young stars of baseball, who is the last remaining on-field link to the Sox of 2013. That was the year of Boston Strong at Fenway Park, as the team and the city spent the entire season honoring those who had died in the Boston Marathon bombing in April that year, all the way through the night they closed out the Cardinals in Game 6 of the World Series.

They didn’t run the Marathon last April because of COVID. They ran it on Monday in Boston. Part of the magic of the occasion. Because late Monday night, the Red Sox beat the Rays in the bottom of the ninth to advance to the American League Championship Series -- beat the Rays in their last at-bat the way they had in an epic 13-inning game on Sunday night.

The 2021 Sox start to remind you of Vin Scully’s call of Kirk Gibson’s home run in the 1988 World Series. Scully said that night that in a year that had been so improbable, the impossible had just happened. That is exactly where the Red Sox are right now, now that they will be one of the four teams left standing in baseball this season.

Improbable, trying to make the impossible happen, and get the Red Sox their fifth World Series in this century, one that would be every bit as improbable as the one they got in 2013 when they built a team around the great David Ortiz with grinders like Jonny Gomes and Shane Victorino, just to name a couple. And a kid named Bogaerts, of course, who had just turned 21 that October.

This is what Alex Cora, whose work with this team has been brilliant this season, on and off the field, said about it all after Kiké Hernández had knocked in Danny Santana with the winning run that meant the Sox get to keep playing:

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

They started the season being swept at home by the Orioles. But the Sox immediately turned the early season around with a sweep of -- wait for it -- the Rays at Fenway, and got themselves to first place and stayed there a good long while. But then they stumbled badly after the All-Star break, and nearly lost the chance at a special season when COVID tried to flatten them coming out of August and into September, eleven players and coaches testing positive at one point.

They came back. Again. But got flattened by the Yankees at Fenway the second-to-last weekend of the season, lost two of three to the Orioles the last week, had to come from 5-1 down against the Nationals on the last Sunday of the regular season to stay out of a play-in game with the Blue Jays. Now they have beaten the Yankees in a Wild Card Game and beaten the 100-win Rays in four games and Cora’s record in the postseason is 15-4. Five-and-oh in clinching games.

Monday night’s game, truly, was their season in miniature. They got ahead, 5-0 -- three of those runs coming on a Rafael Devers home run that would have torn a hole in the roof if they’d been playing at The Trop. But then it was 5-1. Wander Franco, the hot kid for the Rays, hit a two-run homer. It was 5-3. Then the Rays tied it 5-5 in the eighth and had the go-ahead run at second with nobody out before a Rule 5 kid the Red Sox got from the Yankees -- Garrett Whitlock -- came on to get the last six outs of the Rays season. You know who pitched like this as the Red Sox closer in 2013, to again go back there? Koji Uehara. Nobody could touch him that October the way nobody could touch Whitlock on Monday night.

Finally in the bottom of the 13th, Christian Vázquez -- the home run hero of Game 3, as the Red Sox won another of those 2013 postseason kind of games -- squeezed a single into short left, and another Christian, Arroyo, bunted Vázquez to second.

Travis Shaw reached on an infield single. First and third, one out. Then Hernández -- who is hitting .450 this October, having stretches where they can’t get him out the way nobody could get out Ortiz eight years ago -- ripped a liner to left and it was 6-5 at Fenway.

“Here we are, surprising everybody except ourselves,” Hernández said when it was over.

And maybe even themselves sometimes, at least a little bit. Trying to go from the bottom to the top in Boston. Is it possible? Xander Bogaerts knows it is. The improbable chasing the impossible in Boston, one more time.