The victory takes the Catalan club above Real Madrid at the top of the standings.
Ukraine striker Artem Dovbyk scored Girona's opener, and Miguel Gutierrez, Valery Fernandez and Cristhian Stuani added further goals to seal a famous victory at the defending league champions.
Robert Lewandowski and Ilkay Gundogan were on target for Barcelona.
The statement win moved Girona two points ahead of Madrid, who drew 1-1 with Real Betis on Saturday.
Barcelona - who had never previously lost in six league matches against their regional rivals - dropped to fourth, seven points behind Girona and five behind Madrid.
The in-form visitors had won 12 of their first 15 league matches, but misfired in their first big test when they lost 3-0 to Real Madrid at home in September.
There was no such problem against Barcelona, though.
"It's a special victory, it gives us the lead," Girona coach Michel Sanchez said.
"I'm very happy with the result because we faced a great Barca team."
The game between Granada and Athletic Bilbao was suspended after a fan suffered a cardiac arrest and died in the stands.
The match will restart on Monday night from the 17th minute with Athletic leading 1-0 after Inaki Williams had put the visitors ahead in the sixth minute.
Atletico Madrid won for a 17th consecutive time at home with a 2-1 triumph over Almeria.
Alvaro Morata and Angel Correa scored a goal each in the first half before Almeria pulled one back through Leo Baptistao after halftime.
"We know there's still a long way to go," said Atletico forward Antoine Griezmann, whose team sit third with a game in hand over those around them.
"We have to keep playing like this."
Atletico's last setback at home in the league was a 1-1 draw with Getafe in February, while Almeria remain the only team without a win this season.
The Saudi-owned club this week was eliminated by fourth-division team Barbastro in the second round of the Copa del Rey.
Relegation-threatened Cadiz's winless streak in all competitions reached 14 matches after a 1-1 draw with Osasuna.
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