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 quick-fire 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, twisting and turning in the area before slotting in the fifth goal.
Real were utterly dominant and Karim Benzema came off the bench to slot away their sixth goal in the 71st.
Zaragoza remain in the relegation places with 12 points.
SOLDADO DOUBLE
An opportunist early double from Getafe striker Soldado was enough to hold off a Sevilla side who dominated the game.
Soldado finished off a sweeping counter-attack to put Getafe ahead after 12 minutes and netted his 10th of the campaign in the 33rd after a misunderstanding in the home defence.
Sevilla turned to substitute Alvaro Negredo and he pulled one back in the 51st, bundling the ball into the net at the far post to end his six-week goal drought.
But profligate finishing and the saves of visiting goalkeeper Jordi Codina made it three games in a row without a win for Sevilla at the Sanchez Pizjuan.
Earlier, Fernando Llorente powered Athletic Bilbao to a 2-0 home victory over Osasuna, lifting his side to sixth in the standings with 26 points.
The Spain striker set up Fran Yeste to tap in the opener inside the first minute at San Mames, and then turned to score with a superb effort from the edge of the area in the 12th.
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