The Galaxy overcame the two-time MLS champions' stubborn defence to progress at the Home Depot Centre, a Beckham free-kick in the first half of extra-time setting up the goal which broke the deadlock in a Western Conference Championship game halted for more than 30 minutes during regular time as the area south of Los Angeles was twice plunged into darkness by a power outage.
The England midfielder, who joined the Galaxy from Real Madrid in July 2007, had helped the LA team reach their first post-season since 2005 and he sent in a 104th minute free-kick that found its way to veteran defender Greg Berhalter to fire home.
Landon Donovan added a second from the penalty spot soon after and the Galaxy moved on to next weekend's MLS Cup final in Seattle against either Chicago Fire or Real Salt Lake, who will contest the Eastern Conference final later today.
The first stoppage came in the 18th minute when the floodlights failed as the Carson neighbourhood was hit by a blackout.
The players were kept on the pitch by referee Terry Vaughan during the delay but play did not resume for another 18 minutes.
Beckham had the first clear-cut chance after the resumption, whipping in a curling free-kick from 25 yards out that a diving Houston goalkeeper Pat Onstad turned around his post in the 26th minute.
The Galaxy were enjoying the better of the chances and Landon Donovan saw his 20-yard shot saved by Onstad a minute into the second half before Houston's Andrew Hainault fired from 30 yards and was denied by a diving Ricketts two minutes later.
Then came the second power failure, in the 51st minute, which halted play for a further 16 minutes.
This time Houston reacted best to the delay and Ching nearly repeated his heroics from the previous round when his strike knocked out Seattle.
His chance came in the 78th minute as he met a cross from the right with a powerful header on the six-yard line only for Ricketts to push onto the crossbar.
The resulting corner saw Hainault head home but referee Vaughan had spotted an infringement in the six-yard box and disallowed the goal to take the game into extra-time.
Then came the breakthrough, Beckham floating in a 104th minute free-kick to the back post, which was headed down by Omar Gonzalez to fellow defender Berhalter who poked it home through a crowd of players past Onstad.
Houston's agony was compounded four minutes later when substitute Alan Gordon was felled in the area by Ricardo Clark, Donovan converting the penalty.
Beckham nearly added a third with a free-kick from 30 yards out that curled past Onstad's top right-hand corner but the Galaxy were home and dry, and the England man has one more game in the MLS before heading to Italy for a six-month loan spell at AC Milan.
Beckham praised his team-mates and Tim Leiweke, president and chief executive of Galaxy owners AEG, for putting the MLS team within reach of their first title since 2005.
"It's so important for us to do well, we've had so many disappointments over the last four years and Tim Leiweke and everybody have put so much behind this team, this club and this franchise and the players are doing them proud," Beckham said.
"We've got a great bunch of guys that are working hard for each other and it's been tough, so we're happy."
Opening goalscorer Berhalter also admitted the delays caused by the power outages had made staying focused difficult.
"It wasn't easy. It was a choppy game with the lights going out and it was hard to get warm again and you just have to stay concentrated.
"I think both teams did that but we got the breaks."
Club captain and second goalscorer Donovan said his team would be watching Saturday's Eastern Conference final between Chicago and Real Salt Lake with keen interest to learn which side the Galaxy would meet next Sunday.
"It will be interesting, we'll watch the game and see what happens. They're two teams we obviously know well having played them a lot but either way we're happy to be there and we think we can win."
