Vazquez's header, officially timed at 49 seconds, was Real Madrid's quickest goal of the season in all competitions.
Real Madrid and Zinedine Zidane are looking to cut their losses and sell their star after a disappointing last few months.
Real Madrid took the lead in the first minute through Lucas Vasquez who nodded home Cristiano Ronaldo's cross.
"We have been keeping an eye on his physical statistics to monitor his recovery, but it is too early for him to play a game of the intensity that we will see in Madrid next week".
Former Brazil striker Ronaldo has urged his old club Real Madrid to make a summer swoop for Neymar, amid suggestions the superstar is unhappy at Paris Saint-Germain despite making a big-money move only last summer.
Toni Kroos curled in a long strike for the third goal, and Ronaldo headed home a corner kick by Luka Modric in the 37th.
- Cristiano Ronaldo is the first player to score a flawless hat-trick in La Liga this season (right foot, left foot and head).
Modi seeks to boost ties with Gulf Arab states during UAE visit
He also called on the Vice President, Prime Minister of United Arab Emirates and Ruler of Dubai , Mohammed bin Rashid Al Maktoum. While speaking on the occasion of foundation stone-laying ceremony, Modi said, "A temple is an agent of peace and harmony".
Jon Bautista pulled one back after the break, but Ronaldo scored his third from close range before Asier Illarramendi's volleyed consolation.
However, the Real Madrid brand ambassador admitted that as of yet, no representative had contacted Neymar.
- Ronaldo has scored in each of his seven league games against Real Sociedad at Santiago Bernabeu (15 goals in total).
"I don't have split loyalties, I hope it is a great game and the best team wins".
Champion-elect Manchester City looked strangely out of sorts during the first 45 minutes of its Premier League clash with Leicester City.
"We are all ready for Wednesday and that is the most important thing".
On Wednesday, Sport brings four managers who could be replacing the Frenchman at the end of the season, and even though there's a new name in the list, Tottenham Hotspur boss Mauricio Pochettino still won't get off the top.