Domínguez scored with his left foot into the lower right of the goal after intercepting a pass from the Periquitos's Sergio García.
Piti never came off during the match. He scored in the 77th minute, took five shots and completed 28 passes. Piti demonstrated his rapport with Leo throughout the match, and connected with the striker for four passes.
With 41 points Los Franjirojos trail Valencia by one for the final Europa League spot, and have compiled a record of 13 wins, 12 losses and two draws on the season.
The Periquitos now sit in 13th in the table with a record of eight wins, 11 losses and eight draws.
Rayo Vallecano were able to convert their 63.4% possession rate into a victory.
The Rayistas's ball control tactics produced seven shots, nine of which were accurate, while also drawing 15 free kicks from fouls and seven corners.
They also completed 351 passes and had 16 crosses in the match.Lass went off due to injury in the 43rd minute and was replaced by José Carlos.
Espanyol had 36.6% of the possession during the match.
Los Blanquiazules had 15 shots, including three on target.
Joan Verdú made his mark on the match for Espanyol after coming on for Víctor Sánchez in the 45th minute, as he took two shots.
Sergio García had five shots for Periquitos, more than any of his team-mates.