Cristiano Ronaldo opened the scoring midway through the first half but also saw a penalty saved by spot-kick specialist Diego Alves early in the second period.
Former Madrid man Dani Parejo looked to have handed Valencia an unlikely point with a stunning free-kick eight minutes from time.
Real stormed forward and needed just four minutes to find the winner when Marcelo cut inside and fired into the far corner.
Real now lead Barcelona by three points at the top of the table with four games to go for both sides.
Barca, though, can move back to the summit of La Liga with victory in the Catalan derby later at Espanyol.
Madrid boss Zinedine Zidane accepted his side nearly paid the price for taking their foot off the gas at 1-0.
“It is true that we were in a comfort zone for 30 minutes, the fans were the same,” said the Frenchman.
“After Valencia scored they started to push the players on once more and it was a completely different match.”
The Brazilian Marcelo added: “We put our heart and soul into it and showed who we are. With the fans behind us we are hard to beat here.”
Zidane recalled eight of the side that started last weekend’s 3-2 El Clasico defeat to Barcelona and had been rested for a 6-2 thrashing of Deportivo la Coruna in midweek.
However, the habitual first team nearly got off to the worst possible start.
Captain Sergio Ramos was returning from suspension after his 22nd career red card in the Clasico and his weak header allowed Santi Mina through on goal inside the first minute.
Keylor Navas came out to block the Valencia striker’s first effort before his follow-up hit the outside of the post.
Fabian Orellana also screwed a great chance wide as Valencia enjoyed the better of the early stages.
However, Ronaldo punished their profligacy in characteristic fashion as he bulleted Dani Carvajal’s cross into the far corner on 27 minutes.
That goal took Ronaldo’s tally in league football to 367 goals to surpass legendary English striker Jimmy Greaves in Europe’s top leagues.
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