HOUSTON -- This was exactly the way Astros manager AJ Hinch scripted it.

Houston ace Gerrit Cole dominated the upstart Tampa Bay Rays for the second time during the American League Division Series as the Astros beat the Rays 6-1 at Minute Maid Park on Thursday, winning the best-of-five series 3-2. It was not easy.

"I'm exhausted after this series against Tampa," Hinch said. "We've got high emotions today. We played an incredibly intense game."

No one was more intense than Cole.

He went eight innings, holding the Rays to two hits and one run -- a solo homer by Eric Sogard -- and struck out 10. It continued a historic run by the big right-hander who, along with teammate Justin Verlander, is viewed as a leading contender for this season's AL Cy Young Award.

Cole held the Rays scoreless over 7⅔ innings in a Game 2 Astros win. His 15 strikeouts in that outing were just two shy of Bob Gibson's record for a postseason game. His 25 strikeouts overall in the series broke the record for the division series round, breaking the mark of 22 held by Verlander and Stephen Strasburg. Gibson (27) is the only postseason pitcher to strike out more hitters in consecutive outings.

Basically, Cole just never allowed a momentum-based Rays offense to get started while he was on the hill.

"The frustrating part is Gerrit Cole is on the mound on the other side and the run he's been on is second to none," Rays manager Kevin Cash said. "That presents its own challenges."

Houston moves on to play the New York Yankees in the AL Championship Series. Game 1 is Saturday night at Minute Maid Park.

The Astros jumped on Tampa Bay starter Tyler Glasnow quickly, collecting five hits and four runs from their first six hitters of the game. Jose Altuve drove in the first run with a single to right, followed by a two-run double from Alex Bregman. Yuli Gurriel drove in the fourth run with a single.

That was plenty of offense with Cole on the mound, who departed after striking out Ji-Man Choi with his 107th pitch of the night to end the eighth.

"I was feeling good," Cole said. "I wasn't thinking about going the distance. I was pretty locked in. It was one pitch at a time."

Cole still has not lost a game since May 22, a streak of 24 straight starts without a loss, during which he has gone 18-0 with a 1.66 ERA and 251 strikeouts, including his two playoff outings.

When Cole retired the Rays in order in the third on a grounder and two fly balls, it marked the first time since Aug. 1 that he had not struck out at least one batter in an inning, a stretch of 73 straight innings. According to Elias Sports Bureau research, it's the longest such streak during the expansion era (since 1961), and second place isn't even close: Pedro Martinez is next on the list with a 40-inning streak in 1999.

"We were tested and responded well," Cole said. "Had to get hit in the face twice. I like the way we answered the bell. Looking forward to the next series."

It was a good thing for Houston that Cole was once again on his game, because after Glasnow's early struggles, the run-stingy Rays locked down the Houston offense, just as they had done for much of the series. Beginning with Glasnow, the Rays set down 13 straight Houston hitters.

The Astros didn't collect another hit until a bloop single from Josh Reddick in the seventh. Houston didn't encounter a Rays reliever it could do damage against until the following inning, when Michael Brantley and Altuve hit back-to-back home runs off Emilio Pagan to provide the final margin.

"The Rays pitching staff was unbelievable to face," Bregman said. "I think the only time the ball looked that small was opening weekend of the year when we faced them. So they were really, really good. It was a really good test."

Still, while Hinch might have liked to see more runs tacked on through the game, the beginning of the contest was what he hoped for. After the Rays got to Houston's starters early in two Tampa Bay wins at Tropicana Field, Hinch called the Rays a "momentum" team. After Game 3, when asked how much of a boost it would be to get a quick lead in Game 4, Hinch said, "Playing with the lead in an elimination game on either side of the elimination is huge."

The Astros ended up playing with the lead for the entire game.

"We feel we are at our best when we got Gerrit Cole on the mound and in control of the game," Hinch said.

Everyone on the Astros, from Cole to AL MVP candidate Bregman to Hinch, went out of their way to congratulate a Rays team that they very much see as equals. Cash said he was understandably proud of his club, which in many respects outplayed the Astros for much of the series. In the end, though, the Astros had Cole and Verlander, and the Rays didn't.

"I think that's fair," Cash said. "That's a lot of it. Yes, that's a lot of it. We caught JV and then Gerrit twice. I mean, elite pitching like that can really quiet good offense. And we have a good offense. They played their part."

After a tough five games, the Astros have a quick turnaround to the next round. The Yankees will arrive on Friday and work out on the field at Minute Maid, several days after wrapping up their three-game sweep of Minnesota in their ALDS series. They are talented and rested, and they've spent the past few days watching the Astros battle Tampa Bay.

Nonetheless, the Astros are where they felt they were headed all along: one series win away from their second AL pennant in three seasons.

"They'll come well prepared," Hinch said. "They're healthy, and it's a quick turnaround. But sometimes I think there's too much gaps in these games. I want to play as many games as fast as we can. When there's any dead time during the playoffs, you get anxious.

"I'll play them tomorrow if they want to play."