Boston’s Justin Turner, right, hugs Rafael Devers after the Red Sox completed a three-game sweep of the Yankees on Sunday in New York. Boston had won 9 of 13 games heading into its road series at Houston. Frank Franklin II/Associated Press

The road to the playoffs goes through Houston.

That’s where the Boston Red Sox opened up a four-game series with the Astros on Monday night, a stretch of games against one of the teams holding a wild-card spot the Sox covet.

Boston arrived in Houston 2 1/2 games behind Toronto, 3 back of Seattle and 3 1/2 behind Houston. They need to leapfrog over two teams to catch the Astros, but it’s their easiest route to the playoffs.

The Red Sox play the Astros seven times over the next 10 days, with three games against the NL West-leading Dodgers separating the pair of series with Houston. By any measure it’s a daunting schedule. It’s also an opportunity.

The games against Houston represent nearly one-fifth of Boston’s remaining schedule. And the Astros represent the best route to the postseason. Even though Dusty Baker’s team sits ahead of the Mariners in the wild-card race, it would be easier for the Red Sox to catch Houston than it is to pass the Mariners.

The Red Sox got themselves in this position by sweeping the Yankees, a team in complete free fall and headed for an offseason overhaul. Boston has gone 9-4 since being swept by the Blue Jays at Fenway Park earlier this month. The Sox were outscored by the Jays 25-8 over three games, and it certainly seemed like the end of any playoff hopes for Boston.

Yet this team has surprised us, for better or worse, all season. They’ve dusted themselves off and brought momentum into Texas. The Red Sox clubhouse was popping with excitement after Sunday’s series-sweeping win over New York, a wild game that saw leads lost and reclaimed, multiple replay challenges on a run that would’ve given the Yankees the lead in the eighth inning, and some of the worst umpiring calls we’ve seen all year.

Manager Alex Cora was ejected in the sixth inning after arguing a third strike call on Trevor Story, one of many calls home plate umpire Junior Valentine seemed to miss. After the game Cora spoke about the argument, and in the process made a new rallying cry for his team.

“We’re grinding here,” Cora told reporters after the game. “We know what’s going on. For us every (expletive) pitch counts. We’re not gonna give up. We’re gonna keep playing. If I get fined, I get fined.”

He will get fined. And the Red Sox will try to take some inspiration from their leader. Cora made those comments wearing a T-shirt from the old “Underdog” cartoon series. It was a not-so-subtle reference to Red Sox President of Baseball Operations Chaim Bloom’s comments at the beginning of the month.

Bloom, in the minutes after the trade deadline, tried to explain his strategy of adding only one major league player (Luis Urías) and not selling off veterans at the deadline. “We’re underdogs this year, right now where we are in the playoff odds.”

The comments caught many by surprise. It’s not often the chief baseball operations executive calls his team an underdog. Yet Bloom was right — the Red Sox have a less than 25% chance of making the postseason according to most websites posting playoff odds. With less than six weeks remaining in the season they need to finish playing nearly .600 baseball to make it.

Boston would have to post that record against some of the best teams in the game. The Red Sox have the toughest remaining schedule in the American League. Yet they have a winning record against teams with winning records this season, one of the many confounding stats in this season filled with wild pendulum swings.

Here’s another one: five times this season the Sox have faced a starting pitcher ranked in the top four in ERA in the major leagues this season. They are 5-0 against them, scoring 24 runs against Gerrit Cole, Nathan Eovaldi, Blake Snell and Justin Steele. They’ve been at their best against the best pitchers in the game.

They’ll face another ace on Tuesday in Houston when Justin Verlander is scheduled to pitch for the Astros.

That’s also when Tanner Houck returns to the mound for the first time since he was hit in the face by a line drive off the bat of New York’s Kyle Higashioka. It’ll be the first time since June that the Red Sox have their entire pitching staff intact.

We’ll see if that’s enough to put together an unexpected finish to the season. They’ve already surprised us be staying in contention this late in the year.

Tom Caron is a studio host for the Red Sox broadcast on NESN. He is a graduate of Lewiston High School.