[GALLO/GETTY]
Manuel Pellegrini's second-placed side climbed to 37 points from 15 games, two short of leaders Barcelona who were in Abu Dhabi winning the Club World Cup.
Sevilla lost ground in third place after a double by Getafe's Roberto Soldado condemned them to a 2-1 home defeat.
Zaragoza arrived at a freezing Bernabeu with caretaker Jose Aurelio Gay standing in after coach Marcelino was sacked last weekend but the league's leakiest defence put up little resistance as they conceded four goals in the first half.
Argentine striker Higuain burst clear to score after three minutes and Dutchman Van der Vaart, playing in place of the injured Kaka, made it 3-0 with a quickfire double.
In the 34th minute, Higuain also claimed a second goal, turning under pressure to lob a spectacular shot into the top corner for his 10th of the campaign.
Cristiano Ronaldo had tried his luck with a number of free kicks and finally got on the scoresheet in the 50th minute, twisting and turning in the area before slotting in the fifth goal.
