The former Chelsea winger entered the field on 83 minutes as a replacement for Raul and almost setup Ruud van Nistelrooy for Real's third goal two minutes later.
After the game, Robben was presented a watch by Real president Ramon Calderon to celebrate his debut and the Dutchman said: "I am very happy. It was a good start. It has been very special.
"The welcome from the fans was fantastic. We have great qualities."