Goalkeeper Vicente Guaita was the hero for the visitors in a tense encounter at the Bernabeu as he produced a string of superb saves to frustrate Cristiano Ronaldo, Angel Di Maria and Karim Benzema.
Real, who play Barca at the Nou Camp later this month, have 79 points from 31 matches, with Barca on 75 after Saturday's 4-1 win at Real Zaragoza and Valencia in third on 49.
Champions Barca, chasing a fourth straight title, can cut the gap to one point with a win at home to Getafe on Tuesday, with Real not playing at Atletico Madrid until Wednesday.
Jose Mourinho's Real side had a 10-point lead over their arch rivals three weeks ago but slipped to consecutive draws against Malaga and Villarreal and were held again on Sunday by a spirited and well-organised Valencia side.
Ronaldo struck a fierce drive against the post in the eighth minute and was again denied by an upright with a deflected effort 11 minutes into the second half.
Valencia had chances too and a 25th-minute Ricardo Costa header and a powerful Tino Costa shot from long range in the 55th also struck the frame of the goal before Iker Casillas brilliantly denied Jordi Alba with just over five minutes left.
Real poured players forward in the final minutes but could not find a way past an inspired Guaita and now need to regroup for the potentially tricky clash at Atletico.
It was their first goalless draw at the Bernabeu in more than five years.
"We still have the advantage and we have to keep going," Real midfielder Xabi Alonso said in a television interview.
"Every point is fundamental now and we are focused on our next game," he added.