The Argentine scored twice and assisted another two, as Jose Mourinho's men picked up the three points in comprehensive fashion.
Arch-rivals Barcelona remain top of the division having also recorded a 5-0 victory over Rayo Vallecano and remain eight points clear of the capital club.
"It is an important win but it is just another game. Barcelona know they cannot lose," Higuain told reporters after the game.
Team-mate Sergio Ramos was also keen to voice his pleasure with the manner of their victory, which extends Madrid's unbeaten run in the league to five games.
“I am pleased with the result. We knew that it was going to be a difficult game and that we couldn’t waste time. We could control the match and we knew how to control each situation," he added.