Fourth-placed Valencia, who have just two wins from their last six games, have 69 points, the same as Sevilla, who are fifth, while Atletico Madrid, in third, have 75.
"It is not a case of saying goodbye to anything, not even to catching Atletico. We will fight until the end,” Valencia coach Nuno Espirito Santo told reporters.
“It is still in our hands, our next game is at home (against Eibar) and we need to win that. There are four games to go and we will approach them with the belief that we will win.”
Rayo took the lead when Valencia goalkeeper Diego Alves flapped at a tame long-range shot by Adrian Embarba and the ball ended up in the back of the net after 19 minutes.
The hosts played their typical attacking game and there were openings at either end but Valencia lacked a finishing touch.
Alvaro Negredo returned to the starting lineup after six games on the bench but was unable to provide inspiration.
Instead it was Parejo, having hit the post with a 25-metre drive early on, who brought Valencia level with a free-kick from the edge of the area after 66 minutes, although there was plenty of controversy in the build-up.
Jorge Morcillo upended Andre Gomes and was red-carded as last man but Negredo, who appeared to be interfering with play as he shielded the ball from a defender without touching it, was in an offside position.
The decision led to tempers rising and Valencia’s Rodrigo Moreno was dismissed for tripping keeper Tono Rodriguez in the 77th minute while Rayo coach Paco Jemez was also sent to the stands for complaining.
With four games left, Barcelona lead the standings on 84 points after their 6-0 win over Granada at the weekend with Real Madrid, who beat Almeria 3-0, two points behind.
Elsewhere, a Francisco Montanes strike for Espanyol sent relegation-threatened Granada to a 2-1 defeat.
A Diego Mainz header brought Andalusian side Granada level after 73 minutes following Sergio Garcia’s opener but Montanes fired home six minutes from the end to give Espanyol victory.
Granada are second from bottom on 25 points, six points from the safety zone.
(This version of the story adds late game and Valencia coach quotes, and the byline)
(Editing by Ken Ferris)
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