The last-kick winner ensured the Blues take a vital lead and two away goals into the second leg at Stamford Bridge in a week's time.
Basel had threatened to arrive in London level after a controversial late penalty saw them equalise, and Luiz says it was crucial to get their noses back in front.
He said: "It was important to score two goals here because Basel are a very good team and their philosophy to play good football is amazing. It is difficult to win here."
But the Brazilian thinks there is still life in the tie, adding: "It is amazing that we scored the second goal with the last kick but we have the second leg and we need to keep our minds strong because it will be another difficult game for us.
"I didn't see the penalty but if the referee gives a penalty then it is a penalty. 1-1 would have been okay but 2-1 is better. We are so happy with this.
"I want to get to the final this year and to do that we have to win the second leg or draw so it is not finished."
Many have questioned the Chelsea players' desire to win the Europa League, but Luiz is adamant it is a trophy they are determined to lift next month.
He continued: "The competition is so important for us. I want to win another European title for my career and for Chelsea."