CLEVELAND — Trevor Bauer chopped slugger Aaron Judge and New York’s other big bats down to size, and Jay Bruce drove in three runs as the Cleveland Indians began chasing their first World Series title in 69 years with a 4-0 victory against the Yankees in the opener of the AL division series Thursday night.

Bauer struck out Judge three times, twice getting him looking. He allowed two hits in 62/3 innings before Manager Terry Francona turned to baseball’s best bullpen, using Andrew Miller and closer Cody Allen to finish the three-hitter.

Allen came in with two on and two outs in the eighth to face Judge, who struck out for the fourth time and angrily snatched at his bat in frustration. Allen worked the ninth for a save.

Bruce connected for a two-run homer in the fourth off Sonny Gray and added a sacrifice fly in the fifth as the Indians began a journey to try and end the majors’ longest Series title drought.

Bauer was Francona’s surprise pick to start Game 1 over Corey Kluber and delivered a performance that started October just right for the Indians.

Kluber, an 18-game winner in the regular season, will start Game 2 on Friday against CC Sabathia.

Coming off their victory against Minnesota in the wild-card game Tuesday night, when Judge homered in his playoff debut, the Yankees came in with momentum.

But Bauer struck out eight and took a no-hitter into the sixth before Aaron Hicks doubled with one out. It was the longest no-hit bid by a Cleveland pitcher in the postseason, bettering Hall of Famers Bob Feller (1948) and Early Wynn (1954), who both went four innings.

Bauer struck out Judge in the first watching a curveball before fanning Gary Sanchez with a pitch way off the plate.

Bauer struck out Judge again in the fourth, but Judge reached on a wild pitch. Bauer regrouped by getting Sanchez to bounce into a double play before freezing Didi Gregorius for his sixth strikeout.

Bauer got help from Jason Kipnis, who made a diving catch to rob Chase Headley in the third. As Kipnis slowly got to his feet, Bauer raised both arms, pumped his fist and screamed to salute his teammate.

Bruce gave the Indians a 3-0 lead in the fourth with a towering homer to right.

After Edwin Encarnacion walked, Gray came inside with a 0-1 fastball and Bruce got around on it. As his shot cut through the fall night, Judge appeared as if he might be able to make a play near the wall, but the 6-foot-7 outfielder could only watch as Bruce’s shot sailed into the seats.

The Indians are 43-9 since Bruce arrived in an Aug. 9 trade from the New York Mets.