Three days after Real's 1-0 extra-time victory over Barca in the King's Cup Final, also at the Mestalla stadium, the Madrid side rested a number of first-team regulars but still proved too strong for their third-placed hosts Valencia.
Higuain rattled in three goals and Kaka grabbed a double after Karim Benzema had opened the scoring as Valencia were torn apart by the pace of Real's counter-attacks.
Home striker Roberto Soldado made it 5-1 after an hour and, as Real eased up, Valencia's Jonas and Jordi Alba grabbed late goals to make the scoreline slightly more respectable.
Pep Guardiola's side moved a step closer to their third consecutive La Liga title and have 88 points with five games left, while Real climb to 80 and Valencia stay on 63.
"The victory was very important," Barca's Villa told Spanish television after ending an 11-match goal drought. "It was very difficult, especially the mental and physical tiredness from the other day, but it's three points more, one game less and the eight-point lead is maintained."
Mourinho had one eye on next Wednesday's Champions League semi-final first leg against Barcelona when he left Cristiano Ronaldo, Xabi Alonso and Pepe on the bench but it hardly made any difference in Valencia.
"We'll keep on fighting in the league until it is mathematically impossible to win it," Mourinho told reporters, describing his team's performance as "spectacular".
He added: "Let Barca win La Liga because of the points they have won rather than because we gifted it to them.
"If we can end the campaign believing we are capable of winning in any stadium, against any team with any group of players we'll have a huge amount of confidence for next season."
Valencia's fans were irate when an almost identical breakaway led to Kaka turning provider for Higuain just before half-time.
Kaka pulled the ball back for Higuain to complete his hat-trick in the 53rd while Soldado's nicely-taken goal, his eighth in four matches, was only a brief respite for the home side.
