For Madrid's 2-0 victory, Brahim Dáz and Joselu scored goals, while Girona overcame a deficit to defeat Villarreal 2-1 and climb to the top of the league.
Following a 2-0 victory over Las Palmas on Wednesday, Real Madrid returned to winning ways. Meanwhile, Girona, who has won six straight games, is leading the Spanish league.
After starting the season with five straight league victories, Madrid lost 3-1 against city rival Atletico Madrid. Brahim Daz and Joselu scored goals for Madrid.
Madrid moved up to second place after the victory at the Santiago Bernabeu Stadium, one point behind Girona, which overcame a deficit to defeat Villarreal 2-1.
With six victories and a draw in its first seven league games, Girona is off to its best-ever start. On Saturday, Madrid will visit Girona.
Six consecutive victories in the first division is not simple, according to Girona coach Michel. "We must savour this occasion. The matchup with Madrid, one of the top clubs in the world, will be crucial.
The defending champion Barcelona, which is two points behind Girona after Mallorca's 2-2 draw on Tuesday, has had its five-game winning streak snapped.
At the Bernabeu, where Madrid was in complete control from the outset, they wasted chance after chance before Daz finally scored with a powerful drive from just outside the penalty area three minutes into first-half stoppage time.
Eight of the host nation's 18 tries in the first half were on target. Las Palmas didn't have any shots on goal until after the half.
After missing many excellent scoring opportunities, newly recruited striker Joselu became increasingly upset until he finally scored with a header in the 54th minute.
Díaz began in place of new signing Jude Bellingham. After scoring six goals in his first seven games with Madrid in all competitions, the 20-year-old midfielder from England started the game on the bench for the first time this year.
Injured forward Vincius Jnior started the game on the bench as well. Early in the second half, he took Joselu's spot.
The need of rotation is fully understood by the players, according to Madrid coach Carlo Ancelotti. "I attempt to manage the squad, and we have to do it in the upcoming games as best we can. That will continue to be the case until the following international break because of how important weariness and the high number of injuries at this time are.
The first-half substitution of defender David Alaba due to what appeared to be a muscular issue caused Madrid to suffer yet another injury setback. Due to chronic knee ailments, the team has been playing without goalkeeper Thibaut Courtois and defender Éder Milito.
For promoted Las Palmas, who defeated Granada in the previous round to earn its first victory of the season, it was their fourth defeat.
GIRONA KEEPS WINNING
Villarreal was defeated by Girona after a comeback, continuing the team's remarkable season.
Dani Parejo scored from the spot to give the hosts the lead in the 49th minute, but goals from Artem Dovbyk and Eric Garca in the 56th and 61st minutes gave Girona the advantage.
The season began with a 1-1 tie for Girona, which is owned by Manchester City's parent company, City Football Group, at Real Sociedad.
Villarreal has lost all three of its games across all competitions.
Other results
Athletic Bilbao, who finished in fourth place, and Getafe drew 2-2 at home; Cadiz and Rayo Vallecano were tied at 0-0.
Valencia fell to host Real Sociedad 1-0.