Dynamo defender Jermaine Taylor, right, challenges Galaxy forward Landon Donovan for the ball. (LUCY NICHOLSON/Reuters)

The Los Angeles Galaxy had been MLS’s best team from almost the start of the season eight months ago, but the final act Sunday night was a maddening exercise.

Finally, after 72 minutes of spellbinding possession and agonizing misses, the Galaxy broke through on a wonderful sequence involving its three superstars, culminating with Landon Donovan’s goal, to upend the Houston Dynamo, 1-0, for its third MLS Cup title.

“We struggled in our finishing,” Coach Bruce Arena said, “and Landon got it done for us.”

Robbie Keane, Ireland’s national team striker, gathered English superstar David Beckham’s flicked header and broke down defender Bobby Boswell with misdirection and footwork.

Donovan, the 2010 U.S. World Cup hero, made a sharp run into the box and, with an instinctive touch that has helped define his sensational career, one-timed Keane’s pass with the outside of his right foot. The ball floated just over goalkeeper Tally Hall’s left hand and settled into the far corner, delighting a sellout crowd of 30,281 at Home Depot Center.

David Beckham of the Galaxy reacts after a goal by Landon Donovan. (Jeff Gross/Getty Images)

The outcome was particularly satisfying for Beckham, whose signing with MLS in 2007 drew worldwide attention but had yet to yield a championship. His contract expires this year, and he has yet to decide whether to return to the Galaxy or resume his European career.

“I might talk in past tense every now and again, but it doesn’t mean I’m not coming back,” said Beckham, 36, who won championships at Manchester United and Real Madrid and was an MLS Cup runner-up two years ago. “It’s been an amazing five years. It’s been the most enjoyable time of my career here in America. This has just topped it off tonight.”

During the postgame merriment, Galaxy supporters chanted, “We want Beckham!” With three of his children in tow and a Galaxy scarf draped over his shoulder, Beckham appeared to wipe away tears. A hamstring injury had limited his training time last week, and after the game, he joked that the celebratory beer and champagne had numbed the pain.

It was also a special moment for Arena, who won MLS crowns with D.C. United in 1996 and ’97 before guiding the U.S. national team at two World Cups.

“I have a ton of respect for Bruce and what he’s done in that locker room to keep that team focused and continue to be winning games throughout the year,” said Dynamo Coach Dominic Kinnear. “MLS is full of ups and downs. I don’t think they ever had a down period. That was a very determined group.”

The Galaxy (23-5-10) didn’t lose consecutive matches and finished 15-0-5 at home with 10 goals conceded.

Los Angeles was the third — and last — MLS team to reach a championship game at a venue previously set aside as a neutral venue. United won the title at RFK Stadium in 1997 and the New England Revolution fell to the Galaxy at Gillette Stadium five years later. Starting next year, the finalist with the most points in the regular season will host the final.

Landon Donovan and David Beckham of the Los Angeles Galaxy celebrate after defeating the Houston Dynamo. (Stephen Dunn/Getty Images)

On Sunday, Beckham combined with Donovan to conduct a fluid attack that generated a wealth of opportunities in the opening half. The most elegant sequence came in the seventh minute with seven consecutive one-touch passes that ushered the ball to overlapping left back Todd Dunivant for a deflected cross.

Everything was working, except the finishing. The chief culprit was Adam Cristman, who replaced injured Chad Barrett on the front line. His first miss was a 12th-minute header off a Beckham corner kick on which he was unmarked six yards from the target.

Overmatched in the middle of the field, Houston tried to work the flanks, and for a few spells, held proper possession. But the match soon swayed back in the Galaxy’s favor.

In the 27th, Beckham swung a high ball to the back post. This Cristman opportunity was more difficult, but the result was the same: a header off the mark. A minute later, Cristman lost his footing after Donovan supplied him in the box.

The pressure continued to mount. Dunivant’s low crossed skipped through the six-yard box untouched and Mike Magee wasted Keane’s diagonal set-up. The Dynamo, which had upset Sporting Kansas City in the Eastern Conference final, had somehow survived the half without falling behind.

“We didn’t play as well as we wanted to and the mood wasn’t happy,” Kinnear said. “I just told the guys, ‘It’s 0-0, we have a chance. There’s a good possibility we win this game.’ ”

The Galaxy, though, was unrelenting. After Keane’s volley missed the far post by a whisker, Beckham supplied Keane for an angled shot between Hall’s legs. The referee’s assistant, however, had flagged the play offside — a decision that, according to video replay, was incorrect. When the commotion died down, Chris Birchall replaced Cristman and Donovan moved higher in the attack — a strategic move conceived in pregame preparations.

The move paid off in the 72nd minute with the harmonic exchange between Beckham, Keane and Donovan, who scored his 20th goal in 29 career playoff matches and won his fourth MLS title in 11 seasons.

“This has been a long year, a trying year, and I’ve got to say, there are times through it all where you get tired and mentally you wear down,” said Donovan, who overcame various injuries and shuttled between the Galaxy and national team. “But [Arena] keeps us going [and] the way David has played through some pretty serious injuries the last few weeks inspired me a lot and forced a lot of us to just get on with it. It was inspirational.”

MLS notes: The league altered the playoff format for 2012, increasing the number of automatic berths for each conference to five from three and eliminating the four wild-card slots regardless of conference affiliation. Also, the conference finals will consist of two legs instead of one game at the highest seed.

In an effort to emphasize rivalries and reduce travel, MLS will abandon the regular season format of home-and-away matches between all clubs. Under the new plan, teams will play only one match against each club from the other conference. Each team will again play 34 regular season games.

More on the MLS Cup

Soccer Insider: Video of Donovan’s goal