The diminutive forward had a big game, setting up both goals as his team condemned Vancouver to another game without a win.
The Royals grabbed a lead just after after halftime. Plata collected Nick Rimando's long goal kick and played a fantastic cross right onto the head of Luis Gil for the youngster to head home.
The home side doubled its advantage in the 71st minute, Plata feeding Javier Morales to apply the finish following a flowing RSL counterattack.
Vancouver has now failed to win in seven straight league games and sits on a 2-4-3 record. RSL moves up to third in the West with a 4-4-2 showing on the year.