After a bright opening, it was an error by the visitors that cost them the opening goal as Franco Zuculini pounced on a loose pass by Gary Medel to free Postiga, and he showed great skill to skip past Alberto Botia and Andres Palop before rolling the ball home on 36 minutes.
Sapanaru then made it two with a simple header from Victor Rodriguez's free-kick seconds before the break, but Medel redeemed himself somewhat 20 minutes from time as his volley deflected in off Glenn Loovens to halve the arrears.
Despite some late chances for Sevilla substitute Baba Diawara, the hosts held on to move into the top half of the table.
Both sides had managed to get back to winning ways last weekend and there was an air of confidence in an open first half with chances at both ends.
Victor was first to threaten but he could not get enough purchase on his header from Postiga's excellent cross early on before again just failing to get on the end of Zuculini's cross-shot on 26 minutes.
Sevilla should have taken the lead moments later though, as Jose Maria Movilla gifted the ball to Alvaro Negredo on the edge of the area but the usually deadly Spanish international pulled his left-footed shot inches wide.
Victor came close again as Palop was forced into a good low save to turn his effort behind, but the goal was coming and it arrived nine minutes before half-time as Zuculini did well to direct Medel's wayward pass in to Postiga, who knocked the ball past Botia before rounding Palop to slot home his seventh goal of the season for club and country.
Sapanaru then gave the hosts a two-goal cushion in first-half stoppage time as he rose highest to place Victor's free-kick perfectly into the top corner.
Sevilla boss Michel introduced Diego Perotti for Hedwiges Maduro in the hope of sparking a reaction from his side in the second period, and after a slow start they began to create chances in the final quarter.
Manu del Moral should have done better when well-positioned at the edge of the area following a lovely flicked pass by Negredo but his shot lacked the power to trouble Roberto.
The Zaragoza keeper was beaten moments later as, after he had blocked a Baba header from close range, the ball found its way to Medel whose shot was headed straight at Roberto until Loovens' mistimed attempt to clear turned the ball into his own net.
Baba then had a great chance to level with nine minutes remaining but, after breaking clear on goal, he delayed when approaching Roberto and that allowed Javier Paredes to get in a vital touch to take the ball towards his keeper, who managed to palm to safety.