The Gunners defeated Sporting by a narrow margin and are now awaiting the rematch, which will be played next Wednesday on the Island, with a goal advantage.
Arsenal showed a reaction after defeats to Manchester City and Southampton.
"I'm extremely happy. It was a big night and an important moment in the season for us, especially because of the situation we're coming from. I think we had something to prove," said the London giants' coach, Mikel Arteta.
Kai Havertz scored the decisive goal in injury time.
"We had to deserve the win. We had periods of dominance and a lot of situations around the penalty area, but we lacked precision in the finishing – movement, the last pass. However, we took the game to where we wanted to go," concluded Arteta.
