Galaxy won thanks to a Landon Donovan penalty, but only after the chance was created by an incredible inside-out pass from England star Beckham.
The former Manchester United struck a swerving 30-yard ball that finished in the path of Donovan and eventually led to their late spotkick being awarded.
With a shot at the MLS league title still 90 minutes away, Beckham said the Galaxy would be staying calm in the wake of its 1-0 second-leg victory over Chivas.
"We're not going to get too excited. We're happy we're through and we deserve to be through but it's another step forward to what we want to do," Beckham told ESPN.
"It's what we want to do for this franchise, Tim Leiweke, everybody that's supported us all the way through, they deserve this, the fans deserve this and the players definitely deserve it."
Beckham left the game soon after Landon Donovan had scored the winning penalty in the 73rd minute, looking in some discomfort after taking a knock to his back.
"It's very sore but the win helps. It was a big game for us tonight and a strong performance. We defended really well, especially after the last game. Our defenders were excellent and credit to Chivas but we're happy."