Jose Mourinho's team hardly had it all its own way though and it trailed at half-time, but it was able to turn the match around to keep alive its slim title hopes.
Emilio Nsue gave the visitor a sixth-minute lead but striker Higuain levelled on the quarter-hour mark.
Alejandro Alfaro put Gregorio Manzano's side in front again after 21 minutes, but Mallorca lost its grip on the match in the second half as Cristiano Ronaldo, Luka Modric, Higuain and Karim Benzema scored to give a dominant Madrid the three points.
Barcelona, fresh from its UEFA Champions League mauling of AC Milan, takes on Rayo Vallecano at the Nou Camp on Sunday evening (Monday morning AEDT).
Real Sociedad climbed up to fourth place with a 4-1 win over Real Valladolid.
Two first-half goals by Antoine Griezmann and one from Imanol Agirretxe set Sociedad on the way to victory, and Xabi Prieto rounded off the win when he netted shortly after the re-start.
Javi Guerra scored a late consolation goal for the visitor.
Valencia nudged its way up to fifth spot, bypassing Real Betis in the process after beating the team from Seville 3-0.
Betis had defender Antonio Amaya sent off for bringing down Roberto Soldado in the penalty area, and the Valencia striker took the penalty himself to give the home side a 17th-minute lead.
It did not double the lead until the 85th minute, with Junior Paulao netting an own goal, and Jonas added the third in the dying moments.
Borja Fernandez claimed the only goal of the game as Getafe kept its UEFA Europa League hopes alive with victory over Athletic Bilbao.
The decisive moment came in the seventh minute when the midfielder lashed the ball home after Pedro Leon's corner.