The teams drew 0-0 in the opening leg in Carson, California, but it was all Tigres at the start of the second leg in the Liga MX side's home ground of Estadio Universitario in Monterrey.
Nicolás Ibañez was left unmarked in the center of the box and headed home for the hosts' first goal in the ninth minute. Uriel Antuna then finished off a quick counter-attack seconds later to make it 2-0.
Joseph Paintsil cut into the deficit before halftime, using his blazing speed to outrun Tigres' defense, round the keeper and fire into an open net.
The Galaxy had renewed hope to start the second half, but it was Tigres that took advantage of a frenzied opening 15 minutes and scored with a deft header by Rômulo that beat John McCarthy.
Carlos Garcés kept the visitors in the game, and make it 3-2 with over a half-hour to play.