Holding a slender lead following their 3-2 win in Germany last week, the Spanish side made sure of their progression thanks to Cazorla's first-half goal and and Rossi's strike after the break against a spirited Leverkusen side who clawed one back through Gonzalo Rodriguez's late own goal.
Villarreal goalkeeper Diego Lopez was imperious throughout, though, with the Bundesliga side creating the better chances but failing to capitalise as their hosts moved through.
After a tentative opening, Domagoj Vida had a shot from 25 yards but his left-footed effort was easily caught by Lopez.
Renato Augusto also had an attempt for the German outfit but failed to test Lopez any more than his team-mate while Eren Derdiyok's free-kick was similarly tame.
At the other end Villarreal forced their first opening in the 17th minute as Rossi smashed wide of goal from close range.
In the 33rd minute the Yellow Submarine extended their aggregate lead and took the wind out of Leverkusen.
The effervescent Cazorla started and finished it, dropping deep to collect the ball before making his way forward, exchanging a neat one-two with Rossi and sweeping the ball home with his right foot.
Leverkusen looked to hit back immediately as Renato Augusto shot from inside the box only to be denied by the seemingly invulnerable Lopez.
Sidney Sam had another chance for the Bundesliga side before the half was out but fired over the bar from 12 yards. When Carlos Marchena fouled Renato Augusto a minute later, he got up to take the free-kick himself and really tested Lopez for the first time with a powerful shot which the goalkeeper saved brilliantly.
Villarreal once again created something from nothing to rubber-stamp the victory on the half-hour mark, Rossi being fed by Cazorla before creating space and rifling home expertly.
Villarreal defender Gonzalo clipped Renato Augusto as he charged into the box and was lucky not to concede a penalty, though he was booked for his trouble.
He got himself in more bother in the 84th minute, though, when Lopez was finally beaten by his slice into his own net from Stefan Reinartz's cross.
Villarreal 2-1 Bayer Leverkusen: Match Report - view commentary, squad, and statictics of the game as it happened.
Source: DSG
