In an entertaining end-to-end encounter it was the visitors who struck first as Borja Valero swept home Jose Angel's cross on 22 minutes. However Sevilla were level before the break as Bruno could only deflect Jesus Navas' shot into his own net 12 minutes later.
Borja passed up a great chance to retake the lead and Diego Lopez made fine saves from Alvaro Negredo and Navas after half-time, but it was Camunas who settled it with a sweet strike into the top corner at the end of a flowing counter-attack.
Villarreal had started the match in the relegation zone but have improved markedly in recent weeks and it was the visitors who made the better start.
Borja put them in front with a calm finish from Angel's cross midway through the first period and could have doubled his tally moments later but was denied by a brilliant save from Javi Varas.
However the goal seemed to spark Sevilla into life and Lopez made the first in a string of wonderful saves as he tipped Freddie Kanoute's powerful header over on 31 minutes.
Three minutes later, though, the hosts did have their equaliser as Navas skipped past Joan Oriol and fired a shot across the box that was turned into his own net by Bruno.
Villarreal were soon back on the attack and Joselu should have made it 2-1 when he was played in on goal but Varas did well again to narrow the angle before deflecting the ball behind with his legs.
Sevilla's eagerness to push forward was leaving the visitors acres of room to break into and they passed up another two wonderful chances to retake the lead just after the break.
Firstly, Borja played a cute one-two with Cani but inexplicably tried to lay the ball into Joselu's path when clean through allowing Varas to intercept, before another counter-attack ended with Mateo Musacchio hitting the post.
Lopez was soon called into action to keep the scores level at the other end as he pushed Negredo's powerful header from close range out for a corner.
Navas was continuing to cause Oriol all sorts of problems down the right and Lopez again did well to smother the Spain international's shot at the near post before the keeper was slightly fortunate as no Sevilla player could capitalise when he palmed Piotr Trochowski's free-kick back into the heart of the penalty area.
A third goal was always on the cards and it finally arrived when another Villarreal break ended with Cani laying the ball back to the edge of the area for Camunas the power home his first goal for the club.
Sevilla threatened a late rally when Oriol saw two quick yellow cards for fouls on Navas, but Fernando Navarro headed wide when unmarked with the last action of the game as their run without a win stretched to seven league games.