Cole threw seven scoreless innings to win his 19th consecutive decision despite walking five batters for only the second time in his MLB career. The ace pitched out of a bases-loaded jam in the first and stranded nine runners through five innings, boosting his record to 3-0 with a 0.40 ERA in three postseason starts this year.
The 29-year-old right-hander, who is unbeaten in 25 starts since his last defeat on May 22, gave up four hits and struck out seven.
Jose Altuve sparked the Astros' offense with a solo home run in the first inning off Yankees starter Luis Severino. Josh Reddick also belted a solo shot off Severino to give Houston an early 2-0 lead in the second.
In the seventh, Altuve scored on a wild pitch by Zack Britton. Later in the inning, Yuli Gurriel scored Michael Brantley on a sacrifice fly to push the Astros' advantage to 4-0.
Yankees second baseman Gleyber Torres blasted a solo home run in the bottom of the eighth to give New York its lone run of the game.
Severino allowed two earned runs on five hits across 4 1/3 innings. He struck out six and walked three.
Game 4 of the best-of-seven series is scheduled for Wednesday at Yankee Stadium.