CLEVELAND -- Sometimes, a manager has to worry about tomorrow tomorrow.

That was Cleveland Indians skipper Terry Francona's philosophy as he rode his bullpen hard to a 5-4 victory over the Boston Red Sox in Game 1 of the American League Division Series on Thursday night at Progressive Field.

Francona's two most important relievers, Andrew Miller and closer Cody Allen, both pitched multiple innings. Both threw 40 pitches to help Cleveland nail down the victory.

"We wanted to win the game tonight, and we did," Francona said. "Tomorrow might have to be a different design."

Miller said, "At this point, we're all willing to do what it takes to win. You have so much adrenaline going, you find a way."

Roberto Perez, Jason Kipnis and Francisco Lindor homered in a three-run third inning off Boston starter Rick Porcello, turning a 2-1 Boston lead into a 4-2 Cleveland advantage.

"It was a combination of pitches up in the strike zone and a night where this ballpark played extremely small," Boston manager John Farrell said. "We were up in the strike zone, and they made us pay for it."

Neither starter got very deep into the game. Porcello pitched 4 1/3 innings of five-run ball, and Cleveland starter Trevor Bauer gave up three runs in 4 2/3 innings.

However, the Cleveland bullpen was able to preserve the lead. Miller (1-0) relieved Bauer in the fifth inning and calmed things down for the Indians. Miller, acquired from the New York Yankees at the trade deadline, pitched two scoreless innings, allowing one hit and one walk while striking out four.

"That's why we got him," Francona said.

Bryan Shaw gave up a home run to Brock Holt leading off the eighth inning, cutting Cleveland's lead to 5-4. After Shaw retired Mookie Betts for the first out, and with David Ortiz walking to the plate, Francona called for closer Cody Allen.

Ortiz lined a double to center field and was replaced by pinch runner Marco Hernandez, who went to third on a groundout by Hanley Ramirez. Allen struck out Xander Bogaerts to end the inning.

Allen allowed a single but struck out three more in the ninth to end the game. The last strikeout came against Dustin Pedroia, who thought he checked his swing.

"In real time, it's a borderline call," Farrell said. "After you get a chance to look at the video, he swung."

Andrew Benintendi and Sandy Leon also hit solo home runs for the Red Sox. The teams combined for six home runs, tying the ALDS record.

Holt and Kipnis each had three hits.

Bauer, who was Cleveland's Game 1 starter only because Corey Kluber was giving a strained groin an extra day of rest, got off to a bumpy start, allowing up a single and two doubles to the first five batters he faced.

Pedroia led off the game with a double into the right field corner. Holt then lined a single to right, moving Pedroia to third. Bauer retired the next two batters, but Hanley Ramirez ripped a double into the gap in left-center field. Pedroia scored on the hit, and Holt appeared to score as well.

After the runner was ruled safe, the Indians challenged the call, which was reversed, ending the inning.

The Indians evened the score with a run in the second inning on an RBI single by Lonnie Chisenhall.

The 1-1 tie didn't last long. Benintendi, leading off the top of the third, hit a 3-1 pitch from Bauer into the seats in right field to give Boston the lead.

The Indians answered with a three-homer bottom of the third off Porcello. Perez led off the inning by slamming a 3-2 pitch over the right field wall for an opposite-field home run.

Kipnis hit an 0-1 pitch over the right field wall to give Cleveland a 3-2 lead. Lindor followed that with another booming home run into the seats in right field.

"The first one was exciting," Kipnis said. "When I hit mine, we went nuts, and after the third one, our dugout was losing it."

The home run derby continued in the fifth inning. Leon hit Bauer's 3-2 pitch into the seats in right to cut Boston's deficit to one run.

Porcello (0-1) was removed from the game after Perez led off the bottom of the fifth with a single, then went to second on a fly out to left by Carlos Santana.

Drew Pomeranz relieved Porcello, and Kipnis lined the reliever's second pitch into center field for a single, scoring Perez and giving the Indians a 5-3 advantage.

NOTES: Cleveland's Terry Francona owns a career managerial winning percentage of .617 (29-18) in the postseason. That is the second highest in major league history (minimum 25 games), behind only Joe McCarthy at .698 (30-13). ... Indians RHP Corey Kluber, who won the 2014 AL Cy Young Award and is a candidate again this year, will make his first career postseason start in Game 2. He will oppose Boston LHP David Price. ... The Red Sox's 93 wins in the regular season were 15 more than they won last year. That was the largest improvement of any team in the majors this season.