Buendia came off the bench to score a superb winner as Unai Emery’s team recorded their fifth straight win in all competitions.
Rodrigo Bentancur had fired the hosts into a fifth minute lead but Morgan Rogers then scored his first Villa goal of the season to level.
Buendia, who has now scored three goals in his last four games said: "It feels amazing to come here, it's such a difficult place to play and a really difficult opponent.
“At the start of the match they get the advantage, the team showed character to come back and get a win."
"From the start of the season I wanted to show everyone that I wanted to play for this team and for this club and I am glad I do it every game."
Villa’s win pulled them to within two points of the home side, with fixtures against Manchester City and Liverpool to follow in the coming weeks.
Emery’s team look transformed from the one which struggled through the first month of the season and are now unbeaten in six games in all competitions.
Buendia: “We had a bad start, we couldn't feel comfortable to compete at what this competition deserved and after the break we showed different qualities of the team.
"I think we have a really good squad and good players that didn't play today, they have good qualities.
"It is always important to work hard and push to the best shape for the manager. It is important to fight for our place for the manager.
"It was a great quality goal. I tried to find the bottom corner, I know it is hard but we scored the goal and we got the win."