Monday’s start was not Cole’s best — six innings, three earned runs — but he fanned eight and improved his career postseason record to 8-4. The Yankees, he said, have the same combination of skill and sophistication he saw with the Astros the last two seasons.

“We have a lot of really good players, but we have a lot of smart players,” Cole said. “A good, common theme between all the good teams that I’ve played on is a high level of communication, whether we’re talking about the pitchers in the dugout, from the leadoff guy to the nine hole, or whether we’re talking about defense, how we’re pitching somebody, maybe trying to get an edge in terms of shading one way or the other. Just any sort of feedback from anybody facilitating those conversations is huge.”

The Astros took teamwork to troubling extremes on their way to the 2017 World Series title, using an illegal sign-stealing scheme to gain an edge in home games. Their hitters have been scorned, though not suspended, and their defiance was written on Carlos Correa’s T-shirt on Monday: “H-TOWN VS. EVERYONE,” it said.

Yet after the game, in which he homered twice and drove in four runs, Correa seemed motivated less by doubters and more by the sheer joy of playing when the games matter most.

“I want to be in tough spots; I want to be in decisive situations,” Correa said. “I just prepare myself every single day, mentally, so when that situation comes, I stay ready. October baseball, the energy’s just different. I know there’s no fans this year, but still, knowing you win or go home is what drives me.”

With two more wins, the Astros will reach the league championship series for the fourth year in a row. It would be the longest streak in the A.L. since 1998 through 2001 — by the Yankees, of course.