Real eased to a 10th consecutive league victory, and their 14th in a row in all competitions, to cement their three-point lead over second-placed Barca who have played one game more than Jose Mourinho's side.
Champions Barca have stuttered on their travels but they maintained their superb home form against this season's surprise packages Levante, taking their record at the Nou Camp to eight wins and one draw with 39 goals scored and none conceded.
Real have 37 points from 14 matches. Valencia are third, four points behind Barca with a game in hand after captain Roberto Soldado came off the bench to score the winner in a 2-1 victory at home to Espanyol.
Levante are four points further back in fourth.
Mourinho praised his players for their solidity in defence and efficiency in attack but was reluctant to discuss the crunch game against Barca before Real's Champions League match at Ajax Amsterdam on Wednesday.
"The team is winning and we are playing well," said the Portuguese who is bidding to end his former club Barca's three-year grip on the Spanish title.
"We are winning because of our quality, the spirit of the players and our ability on the counter-attack," Mourinho told reporters.
SPECTACULAR MATCH
Argentina winger Di Maria opened the scoring in the 35th minute at the Molinon when he robbed a defender, surged into the penalty area and surprised goalkeeper Juan Pablo at his near post with a swerving low shot from an acute angle.
Joint La Liga top scorer Cristiano Ronaldo added the second in the 65th, the Portuguese forward's 17th league goal of the season, before Brazil full-back Marcelo made it 3-0 in added-time after exchanging passes with France striker Karim Benzema.
Gijon finished with 10 men after Sebastian Eguren was shown a second yellow card in the 80th minute.
Barca's 4-0 win over Rayo Vallecano on Tuesday was a game brought forward because of their participation in the Club World Cup in Japan later this month and Pep Guardiola's side produced another dominant display against Levante whose annual budget is less than 1/20th of the top two Spanish teams.
Former Arsenal captain Fabregas put the home side 2-0 ahead with a low shot and a header before promising B-team player Isaac Cuenca made it 3-0 after 37 minutes.
World Player of the Year Lionel Messi struck a fourth in the 55th minute, putting the Argentina forward level with Ronaldo on 17 league goals, and Chile forward Alexis Sanchez added the fifth just after the hour.
"The feeling [about the 'Clasico'] is very positive," said Barca defender Javier Mascherano. "It's going to be a spectacular match and the whole world is watching and waiting.
"We are playing a great rival who we have faced many times and we have our weapons."
