HOUSTON -- In a must-win game, it makes sense to turn to the pitcher who always wins. If the Astros were looking for some kind of formula that would help them capture Game 5 of the American League Division Series over the Rays, they found it in the simplest of terms.

Gerrit Cole plus Minute Maid Park equals wins.

It's happened over and over again this year in Houston, and it happened on Thursday night in the Astros' 6-1 clinching win over the Rays that punched their ticket to the AL Championship Series with the Yankees, which begins Saturday night at Minute Maid Park.

Cole has been good all year. But at home, he's a little better than good (12-2, 2.63 ERA, 0.79 WHIP, 13.9 K/9 in the regular season). Fortunately for Houston and the 43,418 rollicking fans who packed the ballpark for the clincher, Cole didn't buck any trends while trying to nail down his most important start of the postseason to date.

"When you have Gerrit Cole on the mound, we win," manager AJ Hinch said. "We have. We've kind of proven that. And when he's as dominant as he's been, as prepared as we know he is, it's just an exciting time for our team."

Cole yielded one run on two hits and two walks over eight typically dominant innings. Aided by an aggressive Tampa Bay lineup whose game plan was clearly to jump on early pitches to try to string some hits together, he maintained an efficient pitch count that enabled him to go deep into the game, and possibly finish it.

Cole ended the outing with 107 pitches and top billing as the scariest starting pitcher remaining in the postseason, now that the pool has been whittled down to four teams.

• The Cole hard facts of Gerrit's Division Series dominance

"He’s a bad man," George Springer said.

Cole, who cruised through most of the outing, was aided by a 10-pitch fifth that included two ground-ball outs and a strikeout of Willy Adames. In a 13-pitch seventh, he walked Travis d'Arnaud but soon ended the inning by inducing a 5-4-3 double play on an Avisaíl García ground ball.

"We were shooting for the double play, trying to get the ball on the ground, pick some pitches that either got us a whiff or got us some contact on the ground to let the guys do what they were doing," Cole said, referring to the Astros' defense. "They were so sharp all night, it's hard not to trust them."

• Dress for the ALCS! Get your Astros gear here

To find the last time Houston lost a game at home started by Cole, you'd have to go back nearly five months to May 22, when the Astros fell to the White Sox. Since then, they have won all of Cole's 14 starts at Minute Maid Park, and overall, they’ve won 17 of his 19 home outings.

"Coming to the ballpark gives us great vibes that we're going to have an opportunity to win," Hinch said. "We know he's going to come out hot. We know he's going to get his strikeouts. We know he's going to set a tone. He's intense. There's no mistaking him in what his priority is, which is to get deep in the game and give us a chance to win. And he's done that as much as anybody in baseball."

When the Astros finished off the clincher, Cole tipped his cap to the crowd in an acknowledgement of their support. He did the same after logging his 300th strikeout on Sept. 18.

“This is why we fought all year for 162 games,” Cole said. “They come out in droves all year to support us. They're a baseball-savvy town. They understand big pitches. They understand big plays. And they love to bring the energy.

“I mean, our job is -- we're baseball players, we have to go to work. But when it all boils down, we're just a bunch of kids out there having fun trying to entertain people.”

How much have strikeouts been a part of Cole's game? When he didn't fan anyone in the third inning, that ended a streak of recording at least one strikeout in 73 consecutive innings, regular and postseason, dating back to Aug. 1. That was the longest streak in the expansion era by a whopping 33 games.

"He's unreal, man," Carlos Correa said. "He's on top of the game right now. He’s tough, he’s unhittable. When he’s hitting the spots like he hit today, there’s nobody that can hit him.”

Rays players respectfully concurred.

"Obviously we didn’t want to lose and we wanted to keep playing and go to New York, but Cole was really, really tough again," Adames said. "I don’t know if anyone can get better than that. He was even better than the first start."