The Argentina goalkeeper, whose long-term future at Villa remains in doubt, played a big part in John McGinn's second-half opener 15 seconds after making an important save.
Leon Bailey's late second goal completed a 2-0 win on the night, 3-0 on aggregate, setting up a quarter-final meeting with Bologna who beat Roma 4-3 away for a 5-4 win on aggregate.
Progress keeps Villa's dream of a trophy alive and, after falling short in the Conference League and Champions League in the last two seasons, Europa League specialist Unai Emery must be smelling the scent of a fifth title.
Their journey under the Spaniard has been full of highlights and three successive European quarter-finals are proof of that. Indeed, few would bet against him lifting the trophy in Istanbul in May.
Earlier, Freiburg stormed into the last eight with a 5-1 demolition of Genk while Nottingham Forest beat Midtjylland 2-1 before winning a bizarre penalty shootout 3-0 to advance.
Freiburg rebounded strongly from a 1-0 defeat in Belgium to go through 5-2 while Forest came from 1-0 down with a 2-1 win in Denmark to force the shootout.
Forest levelled the tie with Midtjylland from Nicolas Dominguez's looping header in the 41st.
Ryan Yates got the second in the 52nd from outside the area but the tie was level again from Martin Erlic in the 69th.
Cho Gue-Sung and Aral Simsir hit the left post for the hosts and Edward Chilufya then slipped and fired over, while Forest converted their kicks from Morgan Gibbs-White, Ibrahim Sangare and Neco Williams.
Freiburg now face Spain's Celta Vigo who ousted Olympique Lyon 3-1 on aggregate from a 2-0 victory in France.
Lyon were down to 10 men after 19 minutes when Moussa Niakhaté saw a straight red for a studs-up challenge against Celta's Javi Rueda, who was able to play on and added to his first-leg goal by tapping in the 61st.
Ferran Jutgla wrapped up matters in stoppage time where Lyon then also had Nicolas Tagliafico sent off to end the game with nine men.
Others to advance were Real Betis, Porto and Braga.
In the Conference League, Ismaila Sarr booked Crystal Palace a quarter-final meeting with Fiorentina after an extra-time winner in a 2-1 victory at AEK Larnaca.
The Senegal international also opened the scoring in the 13th minute at the home of the second-placed Cypriot First Division side, where the visitors emerged with more attacking intent than last week's lacklustre goalless draw at Selhurst Park.
Enric Saborit powered home a header to draw the sides level in the 63rd minute, then made things much harder for his teammates when he was sent off for tugging Sarr down 10 minutes later.
Sarr finally broke the deadlock from a Palace corner in the ninth minute of the first period of added time, and came within inches of a hat-trick when he clipped the crossbar twice before the final whistle.
Palace join Mainz, AZ Alkmaar, Shakhtar Donetsk, Rayo Vellacano, Strasbourg, Fiorentina and AEK Athens in the last eight.
with agencies
24°C