Edinson Cavani returned to the Valencia starting XI, following an ankle injury that had kept him out for five games.
Not yet a match winner after any of his five league goals this term, the Uruguayan visibly struggled inside the opening 10 minutes, and instead it was Rayo’s Alvaro Garcia who made the most telling impact.
He swung in a speculative cross from the left, which saw Comesana with acres of space inside the box.
With too much defensive focus on opposite-sided winger Isi Palazon, Comesana couldn’t miss and converted despite a strong Giorgi Mamardashvili hand.
Jose Gaya’s enticing cross was poked goalwards by an outstretched Kluivert right-foot, but unfortunately for him, the base of the post denied him his fifth LaLiga goal of the season.
The dreaded Los Che injury curse struck again at the interval, with Nico Gonzalez having to be replaced despite returning from a previous long-term absence only recently.
Two further attacking reinforcements saw the game swing in the home side's favour, but it was the same old story, as they lacked conviction in front of goal.
Six shots off target preceded a fine Kluivert effort on the volley, but Stole Dimitrievski got down well to keep his side in front.
As the minutes ticked by Valencia thought they had been handed a lifeline from the spot as Mouctar Diakhaby looked to have been fouled when challenging aerially.
On review, referee Jorge Vazquez saw no wrongdoing, but bizarrely pointed to the spot yet again mere moments later, this time for handball on Iván Balliu.
Kluivert nonchalantly rolled the ball home, to claim a vital point that pulled Los Che out of the drop zone - at least for now.