The Gabon international chased down Ben Foster before the goalkeeper's attempted clearance struck him and flew into the net for his 23rd goal of the season.
Aubameyang said: "We are really happy, it was a tough game and at the end we suffered a bit but we did the job and that was important today. It's good.
"I am a guy who always believes in small chances and that was a small chance for me and I tried my best to get to the goalkeeper and I did it and I scored so I am happy. It's a long time I've waited to score a goal like this and I am really happy.
"I think it is a good sign from the team to send to other teams that we are here, present and confident and we want to be in the top four so it's great to go home with the three points."
On a rare away win, he added: "Yes, finally! We suffered a lot playing away but today we fought and it was good from the team and that's why we got the three points."