The Gunners' 3-0 quarter-final first leg triumph last week gave them a vital cushion in the Spanish capital as they made the final four for the first time since 2009, where they will face Paris Saint-Germain.
Bukayo Saka, who missed a first-half penalty, sent Arsenal ahead and although Vinicius Junior levelled the 15-time winners were never close to making up the deficit.
Gabriel Martinelli rubbed salt in their wounds with a stoppage-time winner for Arsenal, who are yet to lift the Champions League trophy.
Arsenal coach Mikel Arteta said he had never been prouder of his team.
"One of the best nights in my football career," Arteta told TNT Sports, as his side chases their first silverware since winning the FA Cup in 2020.
"We played against a team with the biggest history. It has been an inspiration for all of us in this competition.
"To be able to win the tie in the manner we have done - I think we have to be very proud of ourselves.
"The history we have in this competition is so short. The third time in our history of what we have just done, and we have to build on that.
"We had full belief that we could beat this team and the players did it.
"I watched the (PSG) game last night and it was a crazy game," he said of their semi-final opponents.
"I know the manager (Luis Enrique) really well, but let's enjoy tonight. They're a different team now, and they're on an incredible run at the moment."