The 22-year-old lashed in an equaliser five minutes after Lionel Messi's penalty put Barca in front and added a pair of clinical second-half strikes either side of Moise Kean's goal.
Less than 24 hours earlier, reports in Spain suggested an unsettled Mbappe would not force an exit from PSG but would not sign and extension to his contract that expires in June 2022.
"It would be stupid to decide my future on a single match," Mbappe told RMC.
"The truth is that it is about reflecting for the long term.
"I have always said that I am happy here. This sort of match makes me even happier."
The French World Cup winner has netted 21 goals in 29 games during his fourth season playing for his hometown club, as PSG sit second in Ligue 1, one point behind leaders Lille.
Mbappe and his side were on the losing end in last year's Champions League final and the 39-cap international insists he is happy to focus on the club's battles to lift trophies.
"We are very happy. It was a very important game for us. We wanted to come here and win. We did it with style," Mbappe said.
"Now we have an important game on Sunday in the league. Tonight is beautiful but we won nothing.
"I am happy. I always wanted to give the best of myself. There has not always been success. But never in my life will I hide. Today I am paid for the hard work."
Mauricio Pochettino's team now turn their attentions back to the league and a match against Mbappe's former club, fourth-placed Monaco, at the Parc des Princes on Sunday.