Jose Mourinho's team hardly had it all their own way though and they trailed at half-time, but they were able to turn the match around to keep alive their slim title hopes.
Emilio Nsue gave the visitors 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 their 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 their Champions League mauling of AC Milan, take on Rayo Vallecano at the Nou Camp on Sunday.
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 the Basques on their 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 visitors.
Valencia nudged their 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.
They did not double their 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 their Europa League hopes alive with victory over Athletic Bilbao.
The decisive moment came in the seventh minute when the midfielder lashed the ball home following Pedro Leon's corner.
On Friday, Deportivo La Coruna gave their survival hopes a vital boost with a 3-1 victory over 10-man relegation rivals Celta Vigo in the Galician derby.
Sunday's La Liga Preview
Barcelona will be fresh from their comeback Champions League success over AC Milan in midweek and will be hoping to celebrate by routing Rayo Vallecano.
The Catalans romped to a 4-0 win against AC Milan to overturn a two-leg deficit from the first leg and cement their place in the quarter-finals in the Champions League.
Turning their attentions back to the league, Barca will be keen to preserve their 13-point lead over second-placed Real Madrid, who completed a comeback win over Real Mallorca earlier on Saturday night.
Malaga's impending European ban has provided a number of clubs with hope of playing continental football next season.
The Andalucians currently sit fourth - meaning their one-season ban would kick in next term - to give clubs as low as Sevilla in 12th hope of reaching Europe.
Sevilla have a golden chance to boost their bid this weekend when they host a Real Zaragoza side that could have fallen into the drop zone by the time they meet on Sunday.
Atletico are four points adrift of city rivals Real and travel to Osasuna on Sunday to get back within closing distance.
Levante will both look to keep alive their flickering European ambitions as they travel to Granada.
Malaga, who reached the quarter-finals of the Champions League with a 2-1 aggregate win over Porto in midweek, are at home to Espanyol.
Saturday's La Liga Results
Friday's La Liga Result
Saturday's La Liga Results