Neville is still searching for his first league win as Los Che boss as a result, but he will have been greatly encouraged by his team's performance against Los Blancos, who had to play the final 20 minutes with 10 men.
Real Madrid had the first half-chance of the match in the sixth minute, but after Karim Benzema set up Danilo just inside the Valencia box, the Brazilian full-back fired over the crossbar. Down the other end, Paco Alcacer tumbled inside the box under a challenge from both Pepe and Keylor Navas, but the referee was not interested.
Dani Parejo had Valencia's first serious opportunity in the 11th minute, but the skipper glanced a header wide of the post during a period where the visitors were in control of the possession.
Real Madrid took the lead in the 16th minute and it was a special goal as Cristiano Ronaldo's flick played in Benzema and the French striker made no mistake from inside the box to silence the Mestalla.
Valencia had a glorious chance to level just past the 30-minute mark when Rodrigo de Paul found the head of Joao Cancelo with a cross, but the Portuguese fired his header wide of the post from close range.
Andre Gomes was next to come close for the home side as the first period approached its latter stages, but the midfielder missed the target from close range after De Paul had shown wonderful feet outside the box.
Aymen Abdennour also had an opportunity to level late in the half, but the centre-back was eased off the ball by Pepe and the referee was not interested in any penalty shouts from Los Che or indeed the crowd.
Valencia did level in first-half stoppage time, however, when Parejo netted from the penalty spot after Pepe had clumsily brought Gomes to the ground inside the box.
Gomes had the game's next opportunity after finding space outside the box, but his strike in the 63rd minute was palmed over the crossbar by Real Madrid stopper Navas.
An incredible 60 seconds saw Real Madrid have a strong penalty shout turned down when Ronaldo tumbled, before the visitors were reduced to 10 men when Mateo Kovacic picked up a straight red for a lunge on Cancelo.
The referee had a tough task on his hands as tensions continued to rise and the chances continued to arrive as Alcacer came close after closing down a Navas back-pass, before Luka Modric stung the palms of Jaume Domenech.
Real Madrid regained the lead in the 82nd minute when Gareth Bale headed a Toni Kroos free kick into the top corner, but less than one minute later, Valencia levelled as Alcacer headed home from close range after Rodrigo Moreno had beaten Sergio Ramos in the air.
Both sides had incredible chances to take all the points late on, but Alvaro Negredo missed a one-on-one with Navas, before Bale fired over the crossbar in what was the final kick of the match.
The result has left Real Madrid in third position in the La Liga table, now four points off the leaders Atletico Madrid. Valencia, meanwhile, have moved one spot into 10th.