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 pushed forward from the off, Cristiano Ronaldo missing with an early shot and then narrowly failing to get on the end of Lassana Diarra's lofted through ball.
Espanyol had a penalty appeal against the Portuguese rejected, with an element of symmetry later in the half as he had a similar claim turned down in the opposite area.
In the 16th minute Romaric almost ripped up the script when he lashed a loose ball at the Real goal from just inside his own half.
Iker Casillas was well off his line and beaten but the ball went agonizingly wide.
A minute later, the visitors were ahead - Ronaldo touching the ball on to Higuain to stroke the ball home.
A Xabi Alonso free-kick in the 21st minute almost provided a second but after a ricochet in the six-yard box goalkeeper Cristian Alvarez was able to defend his net.
Marcelo tested the keeper with a low drive but despite an unconvincing take he clung on.
Espanyol forward Sergio Garcia made a strong run at goal four minutes before the break but Casillas was down quickly to get fingertips to his shot.
Javi Marquez drilled a long-range shot at Casillas just before the interval, but again he was on hand with the save.
Ronaldo was looking for a goal as the second half got under way, trying his luck from 25 and 20 yards but failing to work the keeper on either occasion.
Joan Verdu forced Casillas into another save from a corner on the hour but the next goal came from the scorer of the first.
Alvaro Arbeloa picked out Higuain's run with a well-judged ball over the top and the Argentina forward allowed it bounce before producing a glorious first-time finish into the far corner.
Cristian Afonso and Vladimir Weiss were lively in attack after coming from the bench for Espanyol but Real would not be contained.
Callejon provided the inevitable third after Ronaldo out-paced the Espanyol defense and teed him up with a one on one, before Higuain produced a deft finish from to secure the match ball.