On a second day of Cup action and Spain's "Reyes" national holiday, Betis were joined in the last eight by Villarreal, Atletico Madrid, Almeria and Real Madrid after holders Sevilla, Barca and Deportivo La Coruna advanced on Wednesday.
Villarreal fought back from two down at home to Valencia to win 4-2 after last month's first leg ended goalless.
Sergio Aguero celebrated this week's signing of a two-year contract extension with a goal in Atletico's 1-1 draw at Espanyol that put the Madrid club through 2-1 on aggregate.
Real's 8-0 advantage over Levante from the first leg was never under threat in the late kick-off despite coach Jose Mourinho fielding a weakened side.
Seville-based Betis showed why they are poised to return to the first division next season with an efficient performance at a half-empty Coliseum stadium to overturn Getafe's 2-1 away win in the first leg.
"We stole the ball from them in their half, which is not an easy task, and we had control of the game," Betis coach Pepe Mel told a news conference.
"We'll talk about Barcelona later because since we got to the dressing room I have been talking to the players about Huesca," he added, referring to their second-division game on Sunday.
Valencia looked to be cruising into the last eight when first-half strikes from Ever Banega and Roberto Soldado put them 2-0 up at halftime at Villarreal's Madrigal stadium.
Italy international Rossi grabbed a second and Villarreal's fourth with a fine individual effor
