Espanyol had the better of the play throughout but were denied in the first-half by Rayo goalkeeper Dani Gimenez and had a couple of strong penalty claims waved away.
Romaric did eventually put his side in front with a calm finish after he was left all alone inside the area from Juan Forlin's pass. The Ivorian also came closest to adding to the scoreline but his fine drive was turned away by Dani.
Rayo started brightly with Espanyol's all-time record goalscorer Raul Tamudo up front and a boisterous home crowd not deterred by the 12 noon kick-off time that has affected crowds across the league so far this season.
Espanyol keeper Cristian Alvarez was called upon to make the first save of the game on 14 minutes as Piti's free-kick evaded everyone and would have sneaked in at the far post but for a strong right handed save from the Argentinian.
The visitors then began to take control of proceedings with Javi Marquez and Joan Verdu pulling the strings in midfield and it was from Verdu's through ball that Sergio Garcia raced clear but his right foot shot from a narrow angle was beaten away by Dani.
Alvaro Vasquez should then have given Espanyol the lead but failed to make contact with a wonderful ball in from Garcia before Rayo were lucky not to give away a penalty as a corner from the left seemed to strike Piti on the arm but nothing was given.
The visitors' frustration at that decision was only compounded when Iglesias Villanueva again failed to point to the spot when Alvarez was brought down from behind by Piti 12 minutes later.
Early in the second-half Tamudo had the chance to score against his old club but Alvarez was out quickly to smother at the striker's feet.
Romaric finally broke the deadlock on 55 minutes as he controlled Juan Forlin's pass inside the area and had plenty of time to pick his sport as he shot past Dani.
Rayo manager Jose Ramon Sandoval tried to change things by brining on Dani Pacheco and Lass Bangoura but it was Espanyol who nearly doubled their lead and Romaric his tally with an excellent left foot shot that Dani just managed to tip over.
Sergio Garcia and Rui Fonte had opportunities to put the game to bed but despite both missing the target Espanyol deservedly held on to record their first win on the road since January 23.