HOUSTON — Trevor Bauer has a heated history with the Houston Astros — trash talk with Alex Bregman, a rocky relationship with Gerrit Cole, and a blown save and loss in Game 3 during the Astros' three-game sweep of the Indians in last year's American League Division Series.

No surprise Bauer brought his best Thursday night.

Bauer pitched eight strong innings, Leonys Martin and Jake Bauers homered off Cole, and the Indians beat the Astros 2-1. Bauer (3-1) allowed one run, four hits and six walks. He struck out three.

"He competed his rear end off," Indians manager Terry Francona said. "As a lineup, they don't go out of the zone and his stuff — his last pitch was 97 or 98. And he had six walks and three strikeouts with that stuff. Their lineup is good. They're balanced, they're deep and he competed like crazy."

He improved to 8-0 in his career against the Astros, including two wins against Cole, his former teammate at UCLA. That doesn't include the three relief appearances Bauer made against the Astros in last year's ALDS.

"I knew I was going to have to mix up some sequences and do things a little differently than I normally did," Bauer said. "I thought it worked OK. They hit some balls hard right at some people."

The Indians right-hander continued his solid first month, giving up two or fewer runs in five of six starts.

"They have great hitters, but you have to give credit to Trevor Bauer," catcher Roberto Perez said. "We moved the ball around. We stand up some guys up and in. We kept them off balance, so I think that was the key."

Martin got the first hit off Cole (1-4) with a solo homer in the third that just made it over the right-field wall. Bauers led off the fifth with a solo home run to left to give the Indians a 2-1 lead.

Brad Hand pitched the ninth for his seventh save.

Cole surrendered two runs and three hits with 10 strikeouts in seven innings.

"I just thought that Robinson [Chirinos] and I were on the same page a lot," Cole said. "Just got into a good flow of the game after some misfires in the first and executed more pitches than not."

Cole bounced back nicely after giving up a career-high nine runs in 4 1/3 innings in his last start Saturday against the Rangers.

"I thought he was very good and threw some good change-ups, excellent fastballs, his breaking ball was good," manager AJ Hinch said. "He got better after the first inning and did exactly what we hoped to keep us in the game."

George Springer tied it at 1-1 in the bottom of the third with a long solo home run to left that flew out of the stadium.

The Astros had an opportunity with runners on first and second in the sixth when Carlos Correa grounded into an inning-ending double play. Correa, however, didn't run on the play, thinking he fouled the ball off his front foot. The umpires convened and upheld the double play.

"Nobody saw it," Hinch said. "I don't really expect guys to see a ball off of a foot from behind the bases. It's pretty far. I was judging it off of Carlos' reaction and change of direction of the ball. It's not reviewable, we didn't have a challenge anyway. But they said that none of them saw it definitively hit his foot."