The 36-year-old English midfielder is now due to play for his first Major League Soccer title in the final game of his five-year contract in Los Angeles.
"We knew it was going to be a difficult game," Beckham said. "We knew we were always going to be creating scoring chances so it was all about stopping them."
Beckham set up Mike Magee for a goal in the 58th minute. American Landon Donovan had earlier scored and Republic of Ireland striker Robbie Keane would go on to get the third for the Galaxy who will face the Houston Dynamo for the championship on November 20.
The match will take place at the Galaxy's Home Depot Center in south central Los Angeles after Houston beat Sporting Kansas City 2-0 in the other semi-final Sunday.
Beckham's cross enabled Magee to score his third goal of the post-season. "When we walked through the tunnel for the second half, we heard some of their players saying we were tired, we were done," Beckham said.
"I think that inspired us. We're happy to be winning the Western final tonight, but we're not getting carried away."
Keane scored in the 68th minute by slipping past Salt Lake defender Jamison Olave then driving a shot into the far corner of the goal to make the score 3-1. He celebrated with a somersault and cartwheel.
Beckham said Keane's goal was key because it gave them some breathing room.
"We just tell him to score. He has always done that his whole career. His goal came at right time it eased the pressure for us," said Beckham.
Beckham said winning an MLS Cup would be comparable to some of the other championships he has been a part of.
"It is my number one priority," Beckham said. "As a professional you always want to be successful. I have done it for most of my career. It always means the same whether it's winning the MLS Cup, the European Cup or La Liga. Every time you pick up the silverware it is the same."
The Galaxy have played in six previous finals, winning two.
Beckham has not said where he wants to play after this season, with France's Paris Saint-Germain and English Premier League sides Tottenham Hotspur and Queens Park Rangers expressing interest. A new deal with the Galaxy is also an outside option.
Alvaro Saborio scored the only goal for Salt Lake.