Jose Mourinho's side let their football do the talking after a controversial week when the Portuguese coach was sent off during Wednesday's 1-1 stalemate at Villarreal for criticising the referee.
Mourinho was banned from the bench for the game at the Bernabeu but two goals each from Cristiano Ronaldo and Karim Benzema and one from Gonzalo Higuain lifted Real to 75 points with nine matches remaining.
Barca have 69 points in second after Lionel Messi's free kick set them on their way to a 2-0 victory at Real Mallorca, the Argentine World Player of the Year's 18th goal in his last nine games for his club.
Pep Guardiola's side, who visit AC Milan in a Champions League quarter-final first leg on Wednesday, had to play most of the second half with 10 men when midfielder Thiago Alcantara was harshly shown a second yellow card for a handball on 57 minutes.
Third-placed Valencia slipped further behind the leaders and pressure increased on their coach Unai Emery after they lost 3-1 at Getafe in the late kick-off to stay on 47 points, three ahead of city rivals Levante.
Real went for all-out attack against 14th-placed Sociedad, with strike partners Benzema and Higuain getting a rare start together and supported by Ronaldo and Kaka.
Benzema set up Higuain for the opening goal in the sixth minute, Ronaldo added a second just after the half-hour and Benzema made it 3-0 five minutes before half-time.
Sociedad pulled a goal back a minute later when Xabi Prieto's long-range effort flew into the top corner after taking a deflection off the head of Sergio Ramos before Benzema and Ronaldo made it 5-1 with goals early in the second period.
CRUISE CONTROL
"The match the other day [at Villarreal] was a strange one and finished in a very tense atmosphere," Real director Emilio Butragueno said in a television interview.
"Today I think we turned in a very complete performance, especially in the first half, and that was good news.
"We still have a six-point lead and if the team performs to its potential I have to say I am pretty optimistic."
No Real player gave the customary interview to Spanish television after the match and the club decided that Mourinho's assistant Aitor Karanka would not hold a post-match news conference.
At the Iberostar Estadio in Mallorca, Messi fired Barca ahead in the 25th minute when the home defence failed to deal with his inswinging free-kick from the right and it flew past goalkeeper Dudu Aouate into the corner of the net.
It was his 35th league goal of the campaign and Ronaldo's brace later in the day means the pair are tied at the top of the scoring chart and closing in on Ronaldo's Spanish record of 40 in a season set last term.
Barca were on cruise control until Thiago's sending off and the champions endured a nervy 20 minutes before a Messi shot cannoned back off Aouate's left-hand post and centre-back Gerard Pique was on hand to slot the rebound into the empty net.
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
‘England have the players to win the World Cup – it’ll be tough for Thomas Tuchel to do a bad job, with the squad he has at his disposal’ Former Three Lions winger backs new boss after gentle qualifying draw
