This was an evenly matched game at the Ciutat de Valencia stadium which saw few openings until a frantic final 10 minutes, but neither team were able to take any of their chances.
Rayo are now four points from safety, but could see the gap between themselves and 17th-placed Elche widen to seven points should Fran Escriba's side beat Almeria on Sunday.
Levante dropped to ninth, level on points with local rivals Valencia.
Andreas Ivanschitz had the first proper attempt of the game, shooting from inside the area after combining well with his team-mates, but his shot was dealt with by Ruben Martinez, who produced a solid performance in the Rayo goal.
The visitors' first attempt on goal was a shot by Raul Baena which struck the outside of the far post, the midfielder trying his luck as the ball bobbled along the edge of the area.
Levante goalkeeper Keylor Navas - the outstanding performer in last week's 3-2 win at Sevilla - dived across his goal to keep out an excellent free-kick from Roberto Trashorras, while his opposite number Ruben recovered well to prevent David Barral taking full advantage of a mishap by Rayo defender Saul Niguez.
Barral did not enjoy his finest evening in front of goal, twice miscuing in the first half and sending the ball hopelessly off target.
The second half was even scrappier than the first, with both sides struggling to create clear goalscoring opportunities until the latter stages of the game.
Saul headed a corner just wide of the near post in the final 10 minutes, while Ruben made a great save to deny Barral in a one-on-one situation.
Baba Diawara also spurned a late chance, striking just beyond the far post from a difficult angle, and Pape Diop sent a last-minute free-kick over the bar and into the stands.