The first leg in Portugal ended 1-1 and the Gunners were under pressure coming into this game. However, Arsenal had the all-important away goal.
The Gunners started the game well when Pierre-Emerick Aubameyang scored the opening goal in the 21st minute.
However, the away side turned the game on its head when Goncalves scored the leveller in the 43rd minute and Ferreira Silva put them in the lead in the 61st minute.
With Benfica leading on aggregate and with two away goals under their belt, the Portuguese side seemed destined to go through to the next round.
Kieran Tierney brought the Gunners back into the game in the 67th minute. However, the away side still had the comfort of the away goals.
Star striker Pierre-Emerick Aubameyang spared the blushes for the home side with his 87th-minute winner.
The goal was checked by VAR for offside and the Gunners will be relieved that their goal was deemed legitimate. The Londoners are now through to the next round of the competition.
The Europa League is their best chance of winning a trophy this season and Arsenal will have to improve defensively if they want to win the competition.
As for Benfica, they will be disappointed to have crashed out of the tournament after coming so close to booking their place in the next round.