- Real Madrid held at Valencia
- Los Che grab late equalizer
- Real stays third in standings
Former Manchester United and England star Neville is still searching for his first win, but this was the best performance by Los Che since he took over, nearly grabbing victory at the death.
Barcelona's disappointing home draw with neighbor Espanyol Saturday had opened the door for Real, but again Rafael Benitez's team failed to take advantage.
The weekend results left its city rival Atletico at the head of the standings by two points from Barcelona and four clear of Real.
Barca, which was involved in the Club World Cup, winning the title, has a game in hand on both its fellow title contenders.
Real twice led, the first time after Karim Benzema scored an early opener following a fine move involving Cristiano Ronaldo and Gareth Bale.
But Valencia leveled on the stroke of halftime as Dani Parejo converted a penalty following a Pepe foul on Andre Gomes.
Real suffered a further blow past the hour mark when Mateo Kovacic was sent off for a clumsy tackle but then looked set to take three points when Bale scored with an excellent glancing header in the 82nd minute.
But the home side salvaged a draw when Paco Alcacer headed in from close range almost immediately.
In injury time it could have got worse for the visitors when substitute Alvaro Negredo had a great chance but shot straight at Keylor Navas.
The in-form Bale took to social media to say he was "absolutely gutted" not to have secured the win for Real, while Benitez, given a warm reception by the home fans as a previous successful manager, believed they deserved the three points.
"We made great effort and could have won the game," he told gathered reporters.