The result lifted coach Michel Sanchez's side two points clear of Real Madrid, who had moved to the summit on Sunday with a 4-1 win over Villarreal.
Girona's regional neighbours Barcelona, the reigning champions, are nine points adrift in third place.
Ukraine forward Artem Dovbyk scored twice and winger Yan Bueno Cuoto dazzled on the right wing in an impressive Girona performance.
Alaves have now gone 24 matches away from home without a win - the worst such run in the club's history.
Girona, in only their second season back in Spain's top flight, took the lead midway through the first half when Dovbyk was on hand to nod home a rebound after Antonio Sivera could only parry Cuoto's effort.
Cuoto was involved again four minutes before halftime when the tricky winger fed Portu, who spun and rifled in a low shot.
With an hour gone, Dovbyk made it 3-0 from the penalty spot after Cuoto was brought down in the box.
It was the Ukraine international's 10th goal in 16 games, with only Real Madrid standout Jude Bellingham ahead of him in the scoring charts.
Sevilla have hired coach Quique Sanchez Flores in a bid to end their poor run of form and move away from the relegation zone.
Flores replaced Diego Alonso, the Uruguayan coach who was fired on Saturday after a 3-0 home loss against Getafe.
Alonso left with the club in 17th place, just outside the relegation zone.
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