Madrid's third draw in five matches had cut its commanding 10-point lead over defending champions Barcelona to four with seven rounds to play.
Barcelona piled the pressure on with a ninth consecutive league victory on Saturday, and Madrid failed to respond as Valencia came close to scoring with two shots that hit the goal-frame in a high-tempo thrilling match that shouldn't have ended scoreless.
Madrid captain Iker Casillas said his team was paying the price for its complacency.
"Madrid can lose this league. There is a great team chasing us," Casillas said. "We can't sit back and live off a 10-point lead we built up in the past. We are facing teams that are also playing for their own goals."
Valencia goalkeeper Vicente Guaita ensured the good result for the visitors with a series of superb saves late on, including denying Angel Di Maria deep into stoppage time.
"We knew it was important to hold off their counterattack and get out on the break ourselves," said Guaita. "The entire team made an excellent effort."
Madrid's stumble places further importance on its visit to Barcelona's Camp Nou in three rounds' time.
The struggling pacesetters visit crosstown rival Atletico Madrid on Wednesday and then welcome last-place Sporting Gijon before the sixth "clasico" match of the season that could go a long way to deciding the title.
"Without a doubt, we expected to win the three points because each point is fundamental," Madrid midfielder Xabi Alonso said. "We still have the advantage, not what we had before, but we have to go forward."
The result also stopped Madrid one game short of setting a club record of scoring in 42 straight games.
Elsewhere, Levante beat Atletico Madrid 2-0 to move into fourth place, Athletic Bilbao edged out Sevilla 1-0 through Fernando Llorente's second-half header, and Mallorca drew 0-0 with Granada.
Even though Valencia entered the match 30 points behind Madrid in the table, the team lived up to its third-place standing by putting up a spirited fight despite having top-scorer Roberto Soldado limited to the final 15 minutes due to physical problems.
"This is a tough ground and Madrid is playing well, taking a point here has merit," said Valencia coach Unai Emery, who had been under growing criticism after his team's recent lackluster run in the league.
"We had our share of the ball and kept faith in our chances. We are satisfied since the team was solid until the end, and we had our options to win throughout."
Cristiano Ronaldo had the first scoring opportunity eight minutes in when he let loose a blistering long-range blast that rattled the woodwork.
Valencia also showed bite early on as defender Ricardo Costa headed against the post with Casillas flat on the ground after having parried Tino Costa' long-range strike in the 25th.
Madrid coach Jose Mourinho sent on Di Maria for striker Higuain Gonzalo at halftime, and the Argentina winger wasted no time in sliding a ball through for Ronaldo to force a one-handed save from Guaita.
Tino Costa again made the home crowd gasp when he blasted against the top corner of the goal-frame in the 55th.
As Madrid's nerves began to show, Valencia looked to take advantage of its opponents runs forward with speedy reinforcements Pablo Hernandez and Jeremy Mathieu, who missed with a long-range shot just after Ronaldo tripped on the ball with only the 'keeper to beat.
Madrid charged forward with Kaka on as a substitute, and Guaita had to stop Di Maria's rising shot and make an excellent pair of reflex saves to repel back-to-back attempts by Karim Benzema from close range in the 78th.
Di Maria had another chance to grab the win just before the whistle, but Guaita again was there to smother his low strike.
"This team and these colors will fight until the end," said Madrid assistant Aitor Karanka, who spoke in place of Mourinho.
On Saturday, Lionel Messi scored his 59th and 60th goals of the campaign to lead Barcelona's 4-1 win at Zaragoza. Also, it was: Getafe 2, Sporting Gijon 0; Rayo Vallecano 6, Osasuna 0; and Espanyol 2, Real Sociedad 2.
Malaga plays Racing Santander on Monday to close round 31.