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Victor Decolongon, Getty Images
Landon Donovan, front, of the Los Angeles Galaxy scored the game's lone goal for the win.

CARSON, Calif. — Landon Donovan scored in the 72nd minute on passes from Robbie Keane and David Beckham, and the Los Angeles Galaxy's three superstars won their first MLS Cup together with a 1-0 victory over the Houston Dynamo on Sunday night.

Beckham won his first MLS championship in the final game of his groundbreaking five-year contract with the Galaxy, who rolled through the postseason to the franchise's third league title after finishing with MLS' best regular-season record.

"I've wanted to be successful for the Galaxy for five years, and tonight, I have that," Beckham said.

Beckham punctuated a solid performance in the MLS Cup with an alert header to Keane, the Irish striker who joined Los Angeles in midseason. Keane made a run and eventually fed Donovan, who struck home his record 20th MLS playoff goal.

"To be honest, the actual goal doesn't mean a lot to me," said Donovan, selected the MLS Cup MVP. "For the last two months, we've just been so determined. I didn't care if it was an own-goal that won it. Winning feels so good."

Beckham lifted Donovan off his feet with a hug after the final whistle, and they joined their teammates for a raucous trophy celebration. Beckham's three sons joined him on the field, with Brooklyn carrying the Cup after they made their way over to the Galaxy's most ardent supporters in the north end of Home Depot Center, where the Galaxy didn't lose all season long.

The English star hasn't decided where he'll play next year, but the Galaxy hope Beckham extends his California sojourn for at least another season. The Galaxy fanatics in the Angel City Brigade supporters' section chanted "We want Beckham!" after the Galaxy's record seventh appearance in the league title game.

"It's been the most enjoyable time of my career in America over the last year, and this just tops it off," said Beckham, whose services are coveted by Paris Saint-Germain and a handful of British clubs. "I've said before, I need to sit back and relax and enjoy this moment, and then I'll figure out what I'm going to do next year. I might talk in the past tense sometimes, but that doesn't mean I'm not coming back."

Los Angeles had the most expensive and highest-profile roster in MLS history, but the Galaxy got full value from their three highest-priced players, particularly in the playoffs. Beckham's assist was his fourth of a stellar postseason, while Donovan scored in each of the Galaxy's final three playoff games, and Keane was a constant offensive threat despite flying across the world in his spare time on Irish national team duty.

Beckham put a stylish finish on the best season of his five-year stint with the Galaxy, finishing second in MLS with 15 assists while spending the entire season in Los Angeles. After the game, Donovan revealed Beckham strained his hamstring during training earlier in the week, while coach Bruce Arena said Donovan has been struggling with undisclosed injuries for several weeks.

"David is a champion," said Arena, the first coach to win three MLS titles. "I've been around great athletes and competitors in my life, and this guy is as good as it comes. Unbelievable desire to win. He's a great teammate, a great person. He's done it all in every country he's been in. What more can you say about a guy like this and what he's brought to this organization and this league in five years? He gutted it out tonight. He obviously wanted to be there."

Beckham grinned at mention of his injury.

"I just had a little bit of champagne and beer, and I can't really feel it anymore," he said.

A sellout crowd of 30,281 cheered Los Angeles past the Dynamo, who hadn't lost in nine games since Sept. 10. Houston struggled for offense in the MLS Cup after losing leading scorer and league MVP runner-up Brad Davis to a torn quadriceps in the Eastern Conference championship.

"It's a well-balanced team," Houston coach Dominic Kinnear said about the Galaxy. "They've been the best in the league from Day 1 to now. They are a deserving champion."

Arena was rewarded for bringing order and professionalism to the Galaxy's messy roster since taking over in late 2008, while Donovan also earned vindication in his fourth career MLS championship. The U.S. national team star gave up his Galaxy captaincy to Beckham early in their tenure, but got it back as his midfield partnership with Beckham matured over the past three seasons.

This championship had been the Galaxy's to lose since early in the season. Los Angeles dominated the league and won the Supporters' Shield with the second-best regular-season record in MLS history, and the Galaxy didn't disappoint in these playoffs after losing in last year's conference final.

Beckham planned to celebrate through the night — but only until dawn.

"I've got school drop-off at 8 o'clock," he said, laughing.