LOS ANGELES -- David Price had heard the criticisms, the questions, the doubts about his ability to perform on the big stage. He had, in fact, been carrying it with him for years. But that is all gone now, erased by a stellar seven-inning, one-run performance at Dodger Stadium on Sunday that helped the Red Sox clinch the World Series in five games with a 5-1 victory over the Dodgers and their ace, Clayton Kershaw.

• Dress like the World Series champs

"It was tough, absolutely," Price said of carrying that burden. "To answer that question in Spring Training ... over and over and over and over, anytime it got to September, playoffs.

"I hold all the cards now. And that feels so good. That feels so good. I can't tell you how good it feels to hold that trump card. And you guys have had it for a long time. You've played that card extremely well. But you don't have it anymore, none of you do, and that feels really good."

:: World Series schedule and results ::

Red Sox manager Alex Cora gambled on Price in Game 5, moving him up to start on short rest in place of left-hander Chris Sale, who ended up closing out the victory. So the gamble worked out on both ends.

Cora had a hunch that Price would be just fine on short rest, on the road, in a potential Series-clinching game -- and if it didn't work out, heck, the Red Sox would have two more chances to get it done at home, with some powerful pitchers lined up to make sure this Series didn't escape them.

As it turned out, there was no need to plan for anything beyond Game 5. No need to turn to Sale or Nathan Eovaldi, or to make any plans for a return trip to Fenway Park for anything other than cleaning out lockers and getting ready for a World Series parade. Price capped a tremendous October with his best start yet on Sunday, holding Los Angeles to one run over seven-plus innings, leading Boston to its fourth World Series title in 15 seasons, and its first since 2013.

Price opened the game by yielding a homer to Dodgers leadoff hitter David Freese. From there, the lefty was dominant, allowing three baserunners until he walked his final batter, Chris Taylor, to lead off the eighth inning.

"I'm very proud of him," Cora said. "There's a lot of people that gave up on him throughout the season. A lot of people that gave up on him after his outing against New York [in the American League Division Series]. But we knew that he's one of the best pitchers in the big leagues, and he cares, he wants to win, and finally -- his World Series win."

Price's World Series numbers -- MVP-worthy, if not for Steve Pearce's Superman-like Series at the plate -- aligned with some of the best performances in Fall Classic history. Price finished with a 1.98 ERA and 10 strikeouts over two starts and one relief appearance, cumulatively allowing three runs and six hits.

• Pearce rides midseason trade to Series MVP

Price became the first pitcher since Hall of Famer John Smoltz in 1996 to allow fewer than seven hits while pitching at least 13 2/3 innings in a World Series.

Given how Price's postseason began -- he pitched poorly in Game 2 of the ALDS, allowing three runs over 1 2/3 innings -- the turnaround was stunning.

What did he prove?

"That I can win a big game," Price said. "I don't know, I haven't reflected on it. I am 33 years old now, and the last time I was in this type of situation was when I was 23 [in 2008, with the Rays]. So a lot of things have changed since then. To be able to come out on top and to be able to contribute in October, that's why I play the game."

It did not start out that way. Price was roundly criticized for his performance against the Yankees, which wasn't the first time he had pitched poorly against the Red Sox's biggest rival. He has sparred with media in the past, and his first two starts in the postseason -- he also struggled in his first start against Houston in the AL Championship Series -- didn't help quiet the critics.

But throughout October, something changed in Price, beginning with his six shutout innings against the Astros in Boston's pennant-clinching game in Houston. Price found a new feel for his changeup and struck out nine Houston batters, while walking none. Astros hitters said later it was the most dominant changeup they had ever seen.

"What I noticed was once he got done with that Houston game, there was just a relief off of him, something off his back," said Red Sox president of baseball operations Dave Dombrowski. "I saw a little different demeanor. The same determination, the same abilities, just that different feeling that he was ready to take charge."

Price followed that outing in Houston with a solid six-inning performance in Game 2 of the World Series, holding L.A. to two runs over six innings. He recorded two outs in the 18-inning marathon of Game 3, and something in Cora's mind told him Price was up to the task to put the World Series to bed in Game 5.

• Price tears up after World Series win

"He enjoys being available," Cora said. "And he was available the whole time, the whole time, from the Division Series to the Championship Series to the World Series. There was a text, 'I'm ready for tomorrow. Count on me. Use me.'"

Cora took him up on the offer, and Price delivered, in the most important game of the year.

"We're World Series champs," Price said. "That's special. This is a very special team. We rallied together all year long starting in Spring Training. So we'll see them all at that duckboat."