Ronaldo inspires Real to win
It was the Portuguese forward's first goal of the season and a third consecutive league victory for Real that lifted them to the top of the table ahead of Wednesday's matches.
Both teams had a player sent off with around half an hour remaining and Espanyol were reduced to nine late on.
Real coach Jose Mourinho criticised the poor state of the pitch after the game and also complained about the packed calendar, Tuesday's match coming after his players were in action in the Champions League on Wednesday and in La Liga on Saturday.
"All things considered I am coming away satisfied because it's not easy playing on a potato field, it's not easy playing every two days and it's not easy playing an opponent who has nothing to lose," the Portuguese said at a news conference.
"Putting all those factors together and despite the fact that my team did not play a good match I am satisfied," he added. "We have to improve but above all we need to rest."
The visitors began brightly on a pleasantly warm night at the Bernabeu and an unmarked Jose Callejon volleyed just wide of Iker Casillas's goal in the sixth minute.
Real responded immediately when Mesut Ozil sent Angel Di Maria clear and the Argentina winger's curled strike was palmed narrowly over the crossbar by goalkeeper Carlos Kameni.
Espanyol's solid start was spoiled just before the half hour when Luis Garcia handled a Ronaldo free kick in the wall and the referee pointed to the spot.
The Portuguese scored with his first attempt but was ordered to retake for what appeared to be encroachment into the area.
Espanyol made an energetic bid for an equaliser in the early stages of the second period and the impressive Joan Verdu forced a sharp save from Casillas in the 53rd.
Real central defender Pepe then picked up two yellow cards in quick succession and Ernesto Galan was shown a straight red shortly after when he chopped down Ronaldo.
The game opened up and both teams had chances before Ronaldo released Higuain with a fine through ball and he beat Kameni with a powerful low shot.
France striker Karim Benzema replaced Higuain and made it 3-0 with almost his first touch, hooking the ball into the net from inside the area.
Espanyol defender Juan Forlin was dismissed late on after picking up a second yellow, apparently for dissent.
Espanyol coach Mauricio Pochettino was clearly furious with the referee after the match but just about managed to restrain himself at his post-match news conference.
"I am not going to give an opinion about the referee, I won't label him with any adjectives," he said.
"The evidence and the television footage is there for all to see. All of Europe and the whole world saw what happened. On days like this you don't feel like talking about football. It's useless."
In the earlier kick-offs, David Lopez put Athletic Bilbao ahead against visiting Real Mallorca just before half-time, Mikel San Jose netted a 62nd-minute penalty and Inigo Perez scored in added time to give the Basque club a 3-0 win.
Osasuna clinched their first victory of the season, coming from behind to beat promoted Real Sociedad 3-1 thanks to goals from Walter Pandiani, Javier Camunas and Carlos Aranda after Raul Tamudo had given Sociedad the lead in the 16th minute.
Champions Barcelona will be without Lionel Messi when they host Sporting Gijon on Wednesday while Valencia can climb back to the top with a win at home to Atletico Madrid.