LOS ANGELES — The Boston Red Sox really are that great.

David Price proved his postseason mettle, Steve Pearce homered twice and Boston beat the Los Angeles Dodgers 5-1 on Sunday to finish off a one-sided World Series in five games.

Long downtrodden during decades of despair before ending an 86-year championship drought in 2004, the Red Sox have become baseball’s team of the century with four titles in 15 seasons.

Alex Cora’s team romped to a 17-2 start and a club-record 108 wins, then went 11-3 in the postseason, dispatching the 100-win New York Yankees and the 103-victory and defending champion Houston Astros in the playoffs. Cora became the first manager from Puerto Rico to win a title and just the fifth rookie manager overall.

Pearce hit a two-run homer on Clayton Kershaw’s sixth pitch. Solo homers by Mookie Betts in the sixth inning and J.D. Martinez in the seventh quieted the Dodger Stadium crowd, and Pearce added a solo drive off Pedro Baez in the eighth.

Pearce, a June acquisition from Toronto, had three homers and seven RBI in the final two games.

After losing to Houston in Game 7 last year by the same 5-1 score, the Dodgers became the first team defeated on its home field in consecutive World Series since the New York Giants by the New York Yankees at the Polo Grounds in 1936-37.

Boston’s Steve Pearce celebrates with J.D. Martinez and Andrew Benintendi after hitting a two-run home run during the first inning in Game 5.

Boston won its ninth title, tying the Athletics for third-most behind the Yankees (27) and Cardinals (11). All that stood between the Red Sox and a sweep was an 18-inning loss in Game 3, the longest World Series game ever. They trailed 4-0 in the seventh inning of Game 4 when ace Chris Sale rose from the dugout bench for a fiery, profane, motivational rant, and woke up for a 9-6 win. Boston never trailed in Game 5.

The 33-year-old Price, a Cy Young Award winner in 2012, long pitched under an October shadow cast by his regular-season success. He had been 0-9 in 11 postseason starts before defeating Astros ace Justin Verlander in the clinching Game 5 of the AL Championship Series. He won his third straight start Sunday and became the first pitcher to beat Cy Young winners in the finale of an LCS and the World Series in the same year.

After allowing two runs over six inning to win Game 2 last Wednesday, Price got two outs in the ninth inning of Friday’s marathon game. He became the first to pitch into the eighth inning of a Series game on one day of rest since the Yankees’ Bob Turley in 1957.

Price gave up a home run to David Freese on his first pitch, then allowed just two more hits – the last a triple to Freese that Martinez lost in the third-inning twilight and allowed to drop behind him in right. Price struck out five and walked two, retiring 14 in a row before a leadoff walk to Chris Taylor in the eighth ended his night after 89 pitches. He tapped his heart several times to Red Sox fans behind the first-base dugout while walking to the bench.

Joe Kelly struck out three straight pinch hitters, and Sale, originally scheduled to start Game 5, fanned three more in the ninth. Sale ended by throwing a slider past Manny Machado, a meager 4 for 22 (.182) in the Series, and raised both arms as catcher Christian Vazquez ran out to jump on him with glee and teammates from the dugout and bullpens followed.

The Boston Red Sox celebrate after winning Game 5 of the World Series over the Dodgers on Sunday in Los Angeles. The Red Sox won 5-1 to win the series 4 games to 1.

While Price rewrote his own legacy, Kershaw was unable to change his. He dropped to 1-4 with a 6.06 ERA in postseason elimination games. Plagued at times by an aching back, the 30-year-old lefty no longer is the dominant pitcher who won three Cy Young Awards, his famous 12-to-6 breaking ball now more 10 to 4:30.

Kershaw allowed four runs and seven hits – three of them homers – in seven innings. He is 9-10 with a 4.32 ERA in 30 postseason appearances, a huge drop from his 153-69 record and 2.39 ERA during the regular season.

He began aggressively, throwing strikes on his first six pitches, and the Red Sox were ready.

Andrew Benintendi hit a one-out single and Pearce pulled a fastball over the middle of the plate and sent it 405 feet into the left-field pavilion.

While the crowd of 54,367 for Dodger Stadium’s final game this year was stunned, Freese woke up fans in the bottom half. He drove Price’s first pitch 402 feet to the opposite field and into the right-field pavilion.

Betts homered on a slider that stayed in the strike zone after going 0 for 13 in Los Angeles this weekend, the first postseason home run of his career coming in his 87th at-bat. Martinez homered in the seventh, driving a fastball to straightway center.

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