They were Higuain's first goals since recovering from back surgery.
"I gained a lot of confidence today. I am very happy; a little tired, but that's normal. There is no better way to return home than with a lot of goals. The hard work and wait were worth it," he told Real Madrid's official website.
"Now it's time to have fun because helping the team and accomplishing our goals are that count. No one was selfish. We played as a team. Now it is time to rest ahead of Wednesday's match, but today we proved that we are in great shape heading into the final stage of the season."