The striker, who joined the Spaniards after leaving Arsenal by mutual consent in January, has scored four league goals in four games for his new club.
He also netted in their Europa League clash with Napoli on Thursday, as they won 5-3 on aggregate.
Aubameyang had been one of Arsenal's key players since joining from Borussia Dortmund in 2018 but, having scored just four goals in the Premier League this season, he left after a bust-up with Mikel Arteta.
Against Bilbao, the Gabon international put his new side ahead after 37 minutes, whilst Ousmane Dembele, who looked set to move to the Premier League in January, doubled their lead.
Summer signings Luuk de Jong and former Manchester United man Memphis Depay made it four in the final minutes, as Barca sit fourth in La Liga.
They are currently 15 points behind leaders Real Madrid with a game in hand but, after a slow start to the season, Xavi will be happy with his side's improved performances in recent weeks.
The additions of Aubameyang, Ferran Torres, and Adama Traore in the January transfer window have been a key part in their upturn in form, as they look to secure Champions League qualification for next season.
After the game, manager Xavi was queried over the future of winger Dembele, who is out of contract in the summer.
The Spaniard though, is just focusing on the French ace's current good form.
"This is not my business," he said. "In football nothing can be ruled out. It is a matter for Dembélé and the club, what I am is happy with him because he is a professional.
"He has made the difference. I see many conditions. Today we have seen the Dembélé that we want and that we all want."
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