Goals from Jeremy Perbet, Javier Aquino and Ikechukwu Uche made it three wins from three for the Yellow Submarine to lift the top-flight newcomers to the top of the standings.
Osasuna, however, are already bracing themselves for another tough campaign having lost all of their fixtures so far.
Jose Luis Mendilibar's Rojillos made a confident start, with Emiliano Armenteros directing a 20-yard drive just over the crossbar after seven minutes.
Oriol Riera then tried his luck for the home side with a powerful header which fell wide of the left post.
However, Villarreal soon came out of their shell and silenced the El Sadar crowd after 22 minutes with the opening goal. Jonathan Pereira's cross fell perfectly in the area for Perbet, who found the bottom-right corner of the net from close range.
Marcelino Garcia Toral's men then strengthened their grip on the match with a second goal on the half hour, a precise left-footed effort from Aquino which he curled low into the net.
It was one-way traffic now and Perbet had the chance to add another before the interval but his teasing shot was well held by Osasuna goalkeeper Andres Fernandez.
Villarreal picked up where they left off at the start of the second half, although a Soriano Bruno header was too weak to trouble Fernandez.
But a third goal followed in the 76th minute thanks to Uche, who made the most of a squared pass from substitute Giovani Dos Santos to tuck the ball home from a few yards out.
There was no way back for Osasuna now, although they were denied a consolation four minutes from time when Jordan Loties's right-footed drive from the edge of the area was brilliantly pushed away by Sergio Asenjo in the Villarreal goal.