1255 GMT November 23, 2019
The visitor led when Karim Benzema finished off a great move involving Cristiano Ronaldo and Gareth Bale, but Dani Parejo equalized with a penalty, BBC wrote.
Real had Mateo Kovacic sent off for a lunging tackle but looked set for a win when Bale headed home.
However, Valencia earned a third point under Neville when Paco Alcacer headed in from close range seconds later.
The home side could have won the game in injury time when substitute Alvaro Negredo was found in space at the edge of the box, but he could only shoot straight at goalkeeper Keylor Navas.
There is no doubt this is the best result of Neville's spell as Valencia boss, following a Champions League defeat, two draws from three La Liga games and a Spanish Cup win over lower league Barakaldo.
Los Che did not look impressive in the opening half hour but Parejo deservedly leveled from the spot after Pepe fouled Andre Gomes.
Once Real went down to 10 men, Neville made some changes, bringing on Rodrigo, who headed a cross into the path of Alcacer to equalize.
Negredo, another substitute, should have sealed a famous win when Alcacer found him in space deep into injury time but he was denied by Navas and Gomes put the rebound wide.
After the game, Neville insisted he wanted to remain at Valencia beyond his six-month contract and said his claim he did not see himself in management long term had been misunderstood.
It appears that Real boss Rafael Benitez is more popular among Valencia fans than his own.
Home supporters unfurled a banner thanking him for a spell in charge that yielded two La Liga titles earlier in the millennium.
Benitez was named Madrid boss in the summer, but it sits four points off city rival Atletico at the top of La Liga and two behind Barcelona, which has a game in hand.
Benitez appeared to anger goal scorer Benzema when replacing him with winger Lucas Vazquez two minutes before Kovacic was dismissed for hacking down Joao Cancelo.
Although it looked like it was going to win it when Bale headed home before Alcacer's quick fire equalizer, Madrid did nowhere near enough to deserve a victory.