Los Blancos were at their very best as they saw off Mauricio Pochettino's men at home with the Brazilian playmaker pulling all the strings for the league leaders
The league leaders grabbed their first goal on 23 minutes when Cristiano Ronaldo finished off a clever move, before Sami Khedira doubled Madrid's goal tally before the break.
Just after the interval Higuain struck from close range before Kaka netted a deserved goal. Higuain put the icing on the cake for the home side with 12 minutes to go, with Jose Mourinho's men appearing odds on to win their first Liga title since 2008.
Madrid made a dominant start to proceedings and it was a surprise that it took until the 23rd minute to open the scoring. After sloppy defensive play by Raul Rodriguez, the centre-back gave the ball away to Mesut Ozil, who played a quick pass into the feet of Higuain. The Argentine flicked into the feet of Ronaldo to sweep home with his left foot from 12 yards out - his 30th Liga goal of the current campaign.
Los Blancos doubled their advantage in the 38th minute as Khedira grabbed his first league goal for Mourinho's men since his arrival at the club in the summer of 2010.
The German midfielder played the ball to Ronaldo who found Ozil, with the playmaker picking out his compatriot in the area who had continued his run. The former Stuttgart man showed great composure to place the ball into the bottom corner past the despairing Kiko Casilla.
The home side could have doubled their lead in first-half stoppage time. Higuain's effort from close range was blocked by the Espanyol custodian, before Ronaldo's long range effort nearly crept in, with Casilla parrying a low shot onto the crossbar after some unorthodox goalkeeping.
Madrid make the perfect start to the second period and put the result beyond doubt on 47 minutes. Kaka picked up the ball before gliding forward and beating the Espanyol offside trap with a precise pass to Higuain, who smashed the ball past the helpless Casilla from six yards out.
It was four for the home team just after the hour mark and Kaka grabbed the goal his impressive performance deserved. Higuain was able to lay the ball off to the Brazilian on the edge of the box, and the former AC Milan man made his way past two Espanyol defenders before placing his shot into the net via the inside of the post.
Madrid made it a five-star evening in the 78th minute as Kaka and Higuain linked up brilliantly once again.
The 30-year-old playmaker showed excellent skill to get past his marker on the left side of the box before sliding the ball into the feet of Higuain, who smashed into the top corner from 15 yards for his 19th goal if the season, to round off a great evening for Los Blancos.
Next up for Madrid is a trip to Betis while Espanyol entertain Rayo Vallecano as they look to bounce back from tonight's heavy defeat.