In-form Olivier Giroud fired the visitors ahead on 16 minutes, before Ashley Barnes equalised with a powerful header.
Giroud netted again on 56 minutes with another well-taken strike for his 13th goal of the campaign, but the Seagulls were level once more through a diving header from Argentinian forward Leonardo Ulloa on his debut after joining from Almeria.
Arsenal, though, finally made sure of a place in the last 16 when Theo Walcott's shot was deflected in following a corner with five minutes left.
"Brighton made it very difficult for us and were sharper than us in the first half. They had a great spirit," Wenger said.
"But in the end we had that little bit of extra quality to get us through. We did our job, but needed to fight until the end."
Wenger admitted his team selection could have come back to haunt him.
He said: "That is a gamble you take and you know it can backfire. You have to rotate knowing that if it doesn't work you will be accused of having made the wrong decision."