Perbet was at fault for the opener, however, as he conceded a penalty right on the half hour mark to hand Elche a glorious chance to break the deadlock.
Damian Suarez stepped up to take the spot kick and made no mistake from 12 yards, firing his effort into the bottom right corner.
Villarreal levelled things up before the break, however, as Jonathan Pereira collected a fine pass before tucking his shot inside the post with just two minutes to go until half time.
The hosts had a chance to take the lead for the first time in the match 10 minutes after the restart as Cani burst into the box, but he made a mess of his finish and missed the target by some distance.
Perbet was the next to come close for Villarreal as he looked to atone for his earlier error of conceding the penalty, but he couldn't keep his shot down as it flew narrowly over the bar.
The hosts could not find a winner in the closing stages, however, as they remain seventh, now one point off the top six.