The Bruins (18-1-2) got to work quickly in the first minute of play, with Lavrusky sending a pass to Caprice Dydasco on the left side. Dydasco drew the goalkeeper out and crossed to Mewis in the center of the box, and Mewis put it away for the early goal, her sixth of the year.
Mewis had a hand in the Bruins' second goal, combining with Sarah Killion to hit Smith for a goal from the right side at 29:41. The goal was Smith's sixth this season and third in as many games.
The Bruins got a scare in the final minute and half of the first half when a shot by Aztec forward Hannah Keane screamed off the bottom of the crossbar, but the ball stayed out the goal, and the shutout remained intact.
UCLA put the game out of reach early in the second half when Lavrusky nailed a curling shot from the left side at 52:46 after a pass from Darian Jenkins.
Bruin goalkeeper Katelyn Rowland earned her 11th solo shutout, making two saves in 90 minutes of play. Melanie Vaughn made seven saves for the Aztecs.
"Getting the goal in the first 43 seconds is how you want to start," said UCLA head coach Amanda Cromwell. "We talked about scoring a goal early, so we were very excited about that. We scored some great goals. San Diego State is a very good team. They won their conference and coming in have been very successful as of late, so all-around it was a good effort."
With the win, the Bruins advance to the NCAA second round on Friday, Nov. 22. UCLA will host Kentucky at 7:30 pm following the South Carolina-Stanford match at 5 pm. San Diego State, which was eliminated from the NCAA Tournament by the Bruins for the second consecutive year, ends its season with a 13-7-2 record.