Yamal's Sunday double, plus second-half goals by Dani Olmo and Pedri against their Catalan rivals, ensured Barca maintained their four-point lead at the top of the table.
Atletico Madrid kept pace by beating last-place Valencia 3-0 with goals from Antoine Griezmann and newly-signed players Julián Álvarez and Conor Gallagher, while Real Madrid had won 2-0 at Real Sociedad on Saturday with goals from Kylian Mbappé and Vinícius Júnior.
Along with Atletico and Madrid, Villarreal were the other team four points behind Barcelona after winning 2-1 at Mallorca on Saturday.
Yamal's goals were his second and third of the season. The 17-year-old Spain international opened the scoring after stealing the ball from a defender and sending a close-range shot into the net in the 30th minute.
He scored again in the 37th minute after picking up a loose ball inside the area.
Olmo's third goal since joining Barcelona this season came from a tight angle in the 47th minute, and Pedri sealed the easy victory with a goal from inside the area with Cristhian Stuani netting Girona's lone reply.
Barcelona played with 10 men from the 87th minute after Ferran Torres was sent-off for a foul.
"To help the team it's important to score the goals and to do whatever is needed," Yamal told reporters afterwards.
"The first match after the international break is always complicated. Now we can start focusing on the match against Monaco (in the Champions League on Thursday)."
Newly-signed Argentina forward Álvarez and England midfielder Gallagher scored their first goals for Atletico Madrid in the team's 3-0 win over last-place Valencia.
Álvarez sealed the home victory in stoppage time after Gallagher had opened the scoring in the 39th and Griezmann had doubled the lead in the 54th.
It was the second consecutive win for Atletico, and third in five league matches.
Earlier on Sunday, 10-man Athletic Bilbao won 3-2 at Las Palmas, who haven't won in 19 straight league games going back to last season. It was the second win for Athletic this season.
Celta Vigo beat Valladolid 3-1 at home for their first win after two consecutive losses.
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