Higuain grabbed the first of the game after 17 minutes and added two more in the second half, with former Espanyol midfielder Jose Callejon also scoring against his old team-mates after coming off the bench.
Three points take Real to third in the Primera Division table with their fourth win of the campaign.
Real coach Jose Mourinho remarked: "We came out of a negative week with a perfect one. It's important because we're aware of our quality, but this is even more important on a psychological level. We managed to leave a bad situation behind, in which we played badly in three games, by earning three victories and scoring 13 goals.
"We're confident again and I'm happy for the team and for those of my men who have hardly played this season. The response of players like Lassana, Albiol and Arbeloa was fantastic."