Betis, who are bottom of La Liga and nine points adrift of the safety zone, had the upper hand in the shootout, but successive misses by Cedrick Mabwati and Nono condemned the green half of the city to a heart-breaking defeat.
Lyon eased through 5-3 against Viktoria Plzen, despite a 2-1 second-leg defeat in the Czech Republic, while a second-half goal from Paco Alcacer earned Valencia a 1-0 win at home to Bulgaria’s PFC Ludogorets Razgrad for a comfortable 4-0 aggregate success.
Dutchman Dick Advocaat, who guided Zenit St Petersburg to the 2007 — 2008 UEFA Cup title, took AZ into the last eight with a goalless draw against Anzhi Makhachkala in Ramenskoye.
Anzhi, propping up the Russian Premier League with one win in 21 games, failed to overturn a 1-0 first-leg deficit.
Their frustrations boiled over in stoppage-time when Karlen Mkrtchyan was shown a red card for a challenge on Steven Berghuis.