CARSON, Calif. — David Beckham flicked a header upfield, finding Robbie Keane on the move. Keane sprinted, stuttered and broke down Houston’s defense before feeding Landon Donovan, who delicately pushed his shot past the diving Dynamo keeper into the far corner of the net.

Everything happened exactly the way the Los Angeles Galaxy drew it up nearly five years ago.

With that dramatic, decisive goal in the 72nd minute of Los Angeles’ 1-0 victory in the MLS Cup on Sunday night, the Galaxy’s trio of superstars earned their first championship together.

When Beckham raised the Cup amid the confetti and cacophony of the postgame celebration, the Galaxy felt justified in every expense and expectation of the experiment they started in 2007 with Beckham’s groundbreaking move to America. In the final game of the English midfielder’s contract, the high-priced, high-profile Galaxy were champions — MLS’ best team all year long, and still dominant at the end.

“I’ve wanted to be successful for the Galaxy for five years, and tonight, I have that,” Beckham said.

Beckham lifted Donovan off his feet with a hug after the final whistle on Los Angeles’ third MLS title. Beckham’s three sons joined him on the field, with 12-year-old 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.

Although the 36-year-old global icon insists he hasn’t decided where he’ll play next year, 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 match as Beckham took a long tour of the pitch with his sons.

“It’s been the most enjoyable time of my career in America over the last year, and this just tops it off,” said Beckham.