Winning 3-0 from the first leg Barcelona were in total control of the tie and they added to their lead on 37 minutes with Argentine ace Javier Saviola firing them in front.
Luis Garcia added a second for the Spanish giants a minute before the break to seal a comfortable passage into the next round for Barca.
Mallorca eased into the next round with a 3-1 aggregate victory over Copenhagen following a 1-1 draw in Spain.
Alejandro Campano added to Mallorca's overall lead on 69 minutes with the opener, but the home side were forced to hold on after Martin Albrechtsen equalised three minutes from time.
Villarreal survived a scare against Torpedo Moscow before securing their place in the third round of the Uefa Cup 2-1 on aggregate after going down to a 1-0 defeat in the Russian capital.
The Spanish side were in pole position to move into the next round after a 2-0 win in the first leg, but Torpedo pushed them all the way with an impressive showing in Moscow.
Torpedo midfielder Igor Senshov reduced the arrears with the opener for the hosts after 71 minutes, but they could not find a second to force the game into extra time.
Click on fixture for full match summary
Torpedo Moscow 1-0 Villarreal (1-2 agg)
Mallorca 1-1 FC Copenhagen (3-2 agg)
Barcelona 2-0 Panionios
