CLEVELAND — Whatever “the book” is, on Thursday night Terry Francona tore out the page on the use of late-inning relievers and put a lighter to it.

With his Indians protecting a one-run lead with two outs in the fifth inning of Game 1 of the American League Division Series against the Red Sox, Francona called on his best reliever, Andrew Miller.

“Nobody ever said you have to be conventional to win,” Francona said. “We wanted to win the game tonight and we did.”

Though shaky at first, Miller got out of a jam of his own making, then resumed being his dominant self — which means the sport’s most feared reliever not named Zach Britton.

The unconventional paid off handsomely. Miller pitched two scoreless innings to settle down the game as the Indians earned a 5-4 victory in front of 37,763 at Progressive Field.

The game featured five homers in the first five innings and six overall, three by each team.

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After Miller — who was obtained from the Yankees in exchange for prospects before the Aug. 1 non-waiver trade deadline — struck out rookie Andrew Benintendi for the second out of the seventh, Francona replaced him with righty Bryan Shaw. Miller’s ensuing walk to the dugout was accompanied by a roar equal to the noise produced by any of the three homers hit by Roberto Perez, Jason Kipnis and Francisco Lindor in the third inning that gave Cleveland a 4-2 lead.

“Miserable,” Kipnis said of what it’s like facing Miller. “I know what those pitches look like. It’s not a fun at-bat for lefties. Or anybody.”

Sandy Leon’s homer to center to lead off the fifth against Trevor Bauer made it 4-3. After Bauer retired Benintendi, who had homered in the top of the third to give Boston a 2-1 lead, and struck out Dustin Pedroia, Francona called for Miller. Brock Holt doubled and Miller walked Mookie Betts as uncertainty rippled through the crowd. Miller, however, struck out David Ortiz, the start of six straight batters retired, four of them by strikeout.

“The playoffs are a different animal,” Miller said. “It’s something that whenever Tito asks anybody to pitch, we’re all going to be ready to go. We’ll find a way.”

Said Francona: “He was up to the task. That’s why we got him.”

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Plenty of drama remained. After Kipnis’ RBI single in the fifth gave the Indians a 5-3 lead, Holt’s leadoff homer off Shaw in the eighth made it 5-4. Cody Allen came in with one out and allowed a double by Ortiz, who was replaced by pinch runner Marco Hernandez. He was stranded at third when Allen struck out Xander Bogaerts.

Allen allowed a two-out single by Benintendi in the ninth but struck out Pedroia to end it.

Bauer allowed three runs and five hits in 4 2⁄3 innings. Red Sox starter Rick Porcello, a favorite for the AL Cy Young Award after going 22-4 with a 3.15 ERA, allowed four runs and six hits in 4 1⁄3 innings, with three of those runs coming in an extremely loud third inning. It marked the first time the Indians hit three homers in one inning in a postseason game since Mark Whiten, Manny Ramirez and Jim Thome did it during the 1998 ALCS against the Yankees.

“We were up in the strike zone,” said Red Sox manager John Farrell, whose club led baseball in runs (878) but struck out 14 times. “And they made us pay for it.”