While the hosts had the better of the play following Neymar's opener, Tomas Pina's dismissal for a dismal second-half challenge on the Brazilian ended slim hopes of Villarreal progression.
Neymar's clever lob, following a delightful Lionel Messi pass, quickly cancelled out Villarreal's away goal from the first leg, although Jonathan Dos Santos' 39th-minute strike against his former club ensured the sides went in at the break level on the night.
Pina - who had earlier ended Sergio Busquets' outing with a studs-up challenge - was at it again shortly after the interval as he threw himself into a dangerous challenge with Neymar to rightly earn his marching orders.
However, Barca's less-than fluent showing before Pina's dismissal and the extent of Busquets' injury will keep Luis Enrique concerned with crucial clashes against Manchester City and Real Madrid coming up this month.
Denis Cheryshev missed the target from close range as Marcelino's side awoke, with Luciano Vietto heading at Marc-Andre ter Stegen and Ikechuwku Uche's strike only finding the side-netting.
Despite being on the back foot, another inch-perfect Messi ball almost led to Barca's second - Andres Iniesta unable to convert - before Dos Santos equalised.
Against his former employers, the midfielder stole in to convert Jaume Costa's deep delivery, with Barca's half ending on a sour note as Busquets left on a stretcher after being caught late by Pina in the build-up.
Suarez made the numerical advantage count when he restored Barca's lead - rounding Asenjo and tapping home - before Neymar's header completed a relatively routine encounter for Luis Enrique's side.
