The Seagulls won 2-1, thanks to Joao Pedro's 98th minute winner from the penalty spot. Pedro had won the penalty, reaching a loose ball first ahead of Harrison Reed before going down from the late challenge.
Hurzeler said afterwards: "Sometimes it’s difficult to describe… there are so many emotions in a moment like that. We were very patient at the end of the game, we didn’t force it, we always believed in ourselves and I think we deserved to win. I am so proud of the guys.
"It helps if you are a fit team because you can play with a high intensity for 90 minutes or more. You can stay focussed and make the right decisions. I wouldn’t say it was the key in this game but fit teams help win games.
"Every game is a learning experience for me and the team. We always reflect on the games so we make the right decisions to continue our journey.
"We are a group who are together and did the basic things right. When you do that you can get results in the Premier League. The fans may be dreaming, but we will keep on working!"
Jan-Paul van Hecke scored Brighton's opener, Hurzeler also said: "I am happy for JP and my set-piece coach. They work hard to create ideas and put a lot of effort into these situations."