Alvaro Negredo gave the visitors the lead after home goalkeeper Diego Lopez had been sent off for a foul on Diego Perotti. Negredo's penalty was saved by Cesar Sanchez but the striker fired home the rebound.
The Yellow Submarine were awarded a penalty of their own 12 minutes later and Giuseppe Rossi made no mistake from the spot, and then Marco Ruben put the home side ahead with a fine finish 18 minutes from time.
The hosts were denied the three points, though, when Alexis headed home an 87th-minute free-kick.
Villarreal were keen to bounce back from their opening-game hammering at the hands of Barcelona and they started brightly with Borja Valero shooting just wide on four minutes.
Sevilla responded well and Lopez had to be alert to deny Perotti and Manu Del Moral as the game flowed from end to end in the opening stages.
However, Lopez's game was over in the 21st minute after he fouled Perotti in the area and was given a straight red card for denying a clear goalscoring opportunity.
Substitute Cesar made a fine save with his first touch from Negredo's penalty but the ball rebounded to the striker and he stroked home into an empty net.
Despite being a man down Villarreal did not go into their shell and, after brilliant play from Rossi to turn away from two defenders, Fernando Navarro brought the Italy forward down for the game's second spot-kick - which Rossi himself converted.
Valero and Negredo both had chances to put their side ahead either side of half-time before Frederic Kanoute had a goal rightly ruled out for offside.
The third goal of the game did eventually come for Villarreal and it was well worth waiting for as Ruben controlled on his chest inside the area before firing an unstoppable shot beyond Javi Varas.
In the final 10 minutes, though, Sevilla started to make their numerical advantage count as Villarreal tired and they equalised with three minutes remaining as Alexis headed home from a free-kick on the right.