Gerrit Cole drew the start for Houston and finished with 12 strikeouts over seven innings, with his only blemish being a solo home run by Indians shortstop Francisco Lindor.
Carlos Carrasco started for Cleveland and gave up six hits in 5 1/3 innings, before leaving the game with the Astros threatening. A 2-run double in the sixth inning by Marwin Gonzalez, off Indians reliever Andrew Miller, gave the Astros a 2-1 lead and put Cole in line for the win.
Then a solo home run to center by Alex Bregman put the 'Stros up 3-1.
Relievers Ryan Pressly and Roberto Osuna shut the door to give the Astros the win.
Astros second baseman, Jose Altuve, came up limping in the sixth inning after a single down the left field line, but stayed in the game.
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During the regular season, Cole had a 15-5 record to go with his 2.88 ERA. Cole also faced the Indians once in May, where he pitched seven innings and allowed three earned runs, but received a no decision. Houston eventually lost in 14 innings by a final score of 10-9.
For the visiting Indians, veteran Carlos Carrasco will take the mound. The 31-year-old right hander was 17-10 this season, with a 3.38 ERA.
Fortunately for the 'Stros, Carrasco hasn't fared well against the home team. In two games, Carrasco went 1-1 against Houston, but also allowed eight earned runs, including three home runs.
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WHAT TO WATCH:
Jose Altuve and George Springer are now tied with Carlos Beltran for the most home runs in Astros postseason history.
Game 1 was the seventh time the Astros have hit at least four home runs in a game, second most all-time among MLB teams. The Yankees are first all-time with 13 games of four or more home runs, but have played 312 more playoff games than the Astros.