Madrid went into halftime a goal down before Higuain and Jose Callejon struck to earn the three points.
"What the coach tells us in the dressing room stays there. Mourinho is a natural motivator and it shows on the pitch. We gave our all after half-time due to things turning out badly for us in the first half. Thank God we managed to win," said Higuain.
"I'm happy for scoring and for earning a victory that keeps us in the lead.
"We knew the match would be complicated and that we would face a Mallorca side different to last year's. We must now savour this victory and rest. There's time enough to prepare for the clash with Barcelona.