Perbet put the team with the distinctive canary-yellow strip ahead in the first minute at their Madrigal stadium before Cani raced down the left wing and crossed for Pereira to tap the ball into an empty net in the 67th.
Sergio Garcia surged clear of his marker and smashed a shot past Sergio Asenjo with 10 minutes remaining to give Espanyol hope but Villarreal comfortably held them at bay to maintain their unbeaten start.
"We began the match very well and the second goal gave us a bit of breathing room," Cani told Spanish television broadcaster Cuatro.
"Everything started badly last season and we were suffering at this stage but we have begun much better this time and hopefully we can finish high up.
"We are coming from the second division but that doesn't mean we are not ambitious and we know we have a good team," added Cani.
The victory for Marcelino's entertaining side, who held Real Madrid to a 2-2 draw earlier this month, strengthened their hold on fourth position with 14 points from six matches.
Espanyol slipped to sixth on 11 points, one behind fifth-placed Athletic Bilbao who recovered from missing a penalty and came from a goal down to win 2-1 at home to Real Betis.
Jorge Molina put Betis ahead in the 62nd minute at the new San Mames stadium three minutes after Benat Etxebarria's spot kick was saved by Guillermo Sara.
Goals from Oscar De Marcos and Mikel San Jose turned the game in Bilbao's favour before another Molina effort bounced back off a post late on.
Getafe secured their second win of the campaign when they beat Celta Vigo 2-0 at their Coliseum stadium in the Madrid suburbs to climb to ninth.
Champions Barcelona and Atletico Madrid were the only two sides to win their opening six matches for a perfect 18 points while Real Madrid are two behind in third place.
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