The Argentine made light of the absence of Karim Benzema with a terrific treble as Jose Mourinho's men proved too good for their Catalan opponents
Madrid, like Barcelona, were playing in black, and just as their arch-adversaries had done earlier in the evening in Gijon, the capital club secured a hard-fought away success.
Higuain was in for the injured Benzema, one of a number of sidelined stars for coach Jose Mourinho, who was also missing Pepe, Ricardo Carvalho, Fabio Coentrao and long-term absentee Nuri Sahin.
In the absence of the two Portugal defenders, right-back Sergio Ramos partnered Spain team-mate Raul Albiol in a makeshift central defensive pairing and the duo did not look entirely secure at the back.
Nor did Espanyol, however, and the locals almost conceded after three minutes, when Cristiano Ronaldo's fierce drive was parried clumsily by Argentine keeper Cristian Alvarez, who must have been mightily relieved to see the ball rebound off his right-hand post and out to safety.
Sergio Garcia blasted over the other end and Ndri Romaric shot wide as Mauricio Pochettino's men threatened again after 16 minutes.
But moments later, they found themselves behind as Ronaldo received the ball from Kaka and set up Higuain on a quick counter-attack, which the Argentine culimated by crashing a powerful right-footed angled drive into the top corner.
Espanyol looked lively despite going behind and Iker Casillas made a fine save to deny Sergio Garcia, but it was all over as a contest as Higuain struck a brilliant second midway through the second period, when he latched onto Alvaro Arbeloa's ball and lashed an unstoppable right-footed drive into the top right-hand corner.
Home fans then applauded as their former hero Jose Callejon was introduced as a substitute late in the game, but just five minutes later the summer signing had hurt his old club by finishing off a quick move after being set up by an unselfish Cristiano.
And Higuain made it 4-0 in added time folllowing a mistake from Hector Moreno to put a gloss on the scoreline and make it a night to remember for the Argentine and Madrid, who now have 13 points - one less than Barcelona.
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