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.
Atletico will play city rivals Real for a place in the semi-finals.
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.
Brazilian playmaker Kaka made his second appearance this season after returning from knee surgery, coming off the bench after the break and heading against the bar in the 83rd minute.
Xisco Munoz had earlier scored from the penalty spot and Sergio curled in a fine free-kick in the 86th to give the home side a 2-0 win on the night.
Almeria were 4-0 up by half-time at Real Mallorca but had to fend off a spirited rearguard action from the Balearic Islanders to hold on for a 4-3 win and an 8-6 aggregate success.
Villarreal will play Sevilla in the next round and Almeria meet Deportivo, who needed a late penalty and extra time to edge past second-division Cordoba on Wednesday.
EFFICIENT PERFORMANCE
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.
All the goals came in the second half, Betis forward Ruben Castro netting twice after Jorge Molina had put them ahead in the 56th minute and substitute Francisco Casquero scoring a consolation goal for Getafe in added time.
"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.
However, the home side blitzed the visitors with three goals in quick succession after the break.
Santi Cazorla scored from close range in the 47th minute, Giuseppe Rossi netted a penalty in the 49th and Marco Ruben finished off a well-worked move in the 63rd.
Italy international Rossi grabbed a second and Villarreal's fourth with a fine individual effor
