Luis Suarez marked his 100th league appearance for Barcelona by scoring his 87th La Liga goal in a 3-0 win over Girona.
His was the only goal scored by a Barcelona player as the Catalan minnows did themselves no favours scoring two own goals in the defeat.
Girona were facing Barcelona for the first time in the top flight and their tight little Montilivi Stadium recorded its highest ever attendance.
Dani Ceballos scored twice on his first league start for Real Madrid as they beat struggling Alaves.
The 21-year-old Spanish midfielder, signed from Real Betis in the summer, held off two defenders before striking home his first.
Alaves, who came into the goal without a point or a goal this season, equalised through Manu Garcia’s header.
But, three minutes later, Ceballos scored his and Real’s second with a low drive from 16 yards.
Also, Atletico Madrid recorded an impressive 2-0 win over Sevilla, thanks to second-half strikes by Carrasco and Antoine Griezmann.
And Malaga won their first point of the season following a pulsating 3-3 draw against Athletic Bilbao. Spanish born Ghanaian striker Inaki Williams scored two goals for the latter.