The Spanish champions moved within a point of leaders Barcelona who face last season's surprise package Girona on Sunday.
Vinicius Junior and Kylian Mbappe both struck from the penalty spot to earn Real Madrid a 2-0 win at Real Sociedad in La Liga on Saturday.
The Spanish champions moved within a point of leaders Barcelona who face last season's surprise package Girona on Sunday.
Real Sociedad hit the woodwork on three occasions before Madrid's second half spot-kicks earned them three points from an end-to-end clash at the Reale Arena.
"It was a tough game, probably we didn't deserve to win because Real Sociedad played very well... but we bore it out, we suffered, we were committed in the tough moments of the game and I value that a lot," said Real Madrid coach Carlo Ancelotti.
"This sacrifice and commitment from a team with such quality, you cannot always find -- and today we found it."
The Italian was without injured midfielders Jude Bellingham and Aurelien Tchouameni, and benched Rodrygo Goes for Brahim Diaz.
After Mbappe netted twice to score his first La Liga goals in his previous outing, all eyes were on the French forward.
The former Paris Saint-Germain striker forced Real Sociedad goalkeeper Alex Remiro into a smart save and had a surging run forward cut short by some last-ditch defending.
Real Sociedad hit the woodwork for the first of three occasions when new arrival Luka Sucic slammed an effort from distance against the bar.
Ancelotti brought on Rodrygo after Diaz suffered an injury and the champions came close through Antonio Rudiger's header, clawed out by Remiro, and an Mbappe effort across the face of goal.
At the other end Real Sociedad forward Sheraldo Becker struck the bar when played in.
- Penalties 'count too' -
Sucic fired a low strike against the post early in the second half as the Basque side lacked luck in front of goal and Madrid inevitably capitalised.
Vinicius fired home from the spot in the 58th minute after Sergio Gomez handled Arda Guler's drive and Mbappe soon followed suit.
The French superstar sent Remiro the wrong way from the spot after Jon Aramburu stood on Vinicius' foot.
Madrid saw the remaining 15 minutes out without stress ahead of their return to Champions League action on Tuesday against Stuttgart.
Mbappe now has three goals in five La Liga matches for Madrid, although two have come from the penalty spot.
"They are linking well, creating a lot of danger," said goalkeeper Thibaut Courtois.
"In open play they're lacking goals a bit, but with them we have a lot of danger up front and we will score a lot of goals.
"Today it was from the penalty spot, but they count too."
Los Blancos last tasted defeat in La Liga in September 2023, going 37 league matches unbeaten since.
Real Sociedad have just one win from five games this season but Imanol Alguacil's team played well.
"We had a great first half, we had a lot of chances, the game was alive," said Real Sociedad's Igor Zubeldia.
"In the second half we started well but the penalty was a tough blow... we were comfortable, it changed the whole game for us."
Earlier Sevilla earned their first victory of the season with a tight 1-0 triumph over Getafe and Villarreal moved provisionally third with a 2-1 win at Mallorca.
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