The Spain striker clipped a sumptuous free-kick into the top corner in the 56th minute at the Nou Camp and smashed home Cristian Tello's unselfish layoff three minutes later as Barca came from behind to win the second leg 3-1 and set up a clash with second division Cordoba.
Coach Tito Vilanova took the chance to give some time on the pitch to players returning from injury and some promising youngsters and rested regulars including Lionel Messi, Xavi, Andres Iniesta, Sergio Busquets and Victor Valdes.
After Barca had won last month's first leg at Alaves 3-0, the Basque club took a surprise 17th-minute lead when Martin Montoya failed to cut out Miki's cross from the right and Borja Viguera nodded past Jose Manuel Pinto.
Adriano levelled in the 35th minute when he exchanged passes with Thiago Alcantara and sidefooted past Alaves goalkeeper Sergio Herrera before Villa struck twice after the break to kill off the tie.
The 30-year-old has gradually been getting back to something close to his best after breaking his leg at the Club World Cup last December and now has 40 goals for Barca since he joined from Valencia at the end of the 2009/10 season.
"We knew we had the advantage but also that they would come out strongly and they pressured us until they got the goal," Adriano said in an interview with Spanish TV.
"But we continued to show the same seriousness and patience to get a positive result," added the Brazilian.
ESPANYOL MISERY
Levante won 4-1 on the night and 4-2 on aggregate but were given a scare by Melilla when they conceded an early goal to the third-tier side that would have sent them crashing out.
A tiny Spanish territory on the north coast of Morocco, Melilla won the first leg 1-0 and were leading 2-1 on aggregate until goals from Roger Marti, Michel and Vicente Iborra from the penalty spot sent Valencia-based Levante through.
Atletico Madrid set up a last-16 meeting with city rivals Getafe when they beat third-tier Real Jaen 1-0 at the Calderon for a 4-0 aggregate success.
Getafe, who won their first leg 4-0, progressed after a 0-0 draw with second division Ponferradina at their half-empty stadium in Madrid.
Valencia will play Osasuna for a place in the quarter-finals thanks to their 3-1 victory at home to Llagostera, another third-tier side, which made it 5-1 on aggregate in favour of the La Liga side.
Valencia defender Adil Rami scored the goal of the night when he drove the ball over the Llagostera goalkeeper's head and into the net from just inside his own half.
Espanyol's misery deepened when they had Javi Lopez sent off in the 25th minute and were thrashed 3-0 at home by Sevilla, the Andalusians progressing 6-1 on aggregate.
Barcelona-based Espanyol, who are bottom of La Liga, fired Argentine coach Mauricio Pochettino after Sunday's defeat against Getafe and appointed Mexican Javier Aguirre in his place.
