Valencia looked to be moving one point behind the league leaders after taking a second-half lead through Rodrigo Moreno, but Barcelona, who controversially failed to take the lead in the 30th minute after the officials failed to spot the ball passing the goal-line, equalised late on through Jordi Alba.
The result means that both teams are still unbeaten in the league this term, with Barcelona remaining four points clear of second-placed Valencia after 13 matches of the 2017-18 campaign.
Valencia's team showed four changes from the one that started last weekend's 2-0 win at Espanyol. Ezequiel Garay came into the centre of defence, while Jose Gaya dropped from a midfield role back into left-back.
Lionel Messi, fresh from signing a new long-term deal with Barcelona, returned to the away side's XI. Thomas Vermaelen, meanwhile, made his first league start of the campaign due to a suspension for Gerard Pique.
Neto was again called into action in the 10th minute to keep out a strike from Ivan Rakitic as the visitors enjoyed most of the ball in the early exchanges.
There was a clear pattern in the opening 25 minutes as Barcelona dominated the possession while Valencia did their best to threaten on the counter-attack, but clear opportunities were few and far between.
There was a hugely controversial moment in the 30th minute, however, when a strike from Messi squirmed through the arms of Neto and dropped past the goal-line, seemingly sending Barcelona 1-0 ahead.
Neither the referee nor the linesman signalled, however, and with goal-line technology absent in Spanish football, Valencia were handed a huge slice of luck as Barcelona were denied a clear goal at the Mestalla.
The dominant visitors continued to search for the opener late in the first period - coming close through Andres Iniesta and Luis Suarez - but the two teams entered the half-time interval on level terms.
Valencia had the first chance of the second half when Guedes fed Zaza in a dangerous position, but the Italian sent his low effort just wide of the far post, before Vermaelen headed just over the home side's crossbar moments later.
Guedes was next to come close for the home side after dancing past the challenge of Nelson Semedo just before the hour, but the attacker could not find a route past Barcelona goalkeeper Marc-Andre ter Stegen.
Valencia did take the lead on the 60-minute mark, however, when Rodrigo turned a low Gaya cross into the bottom corner from close range.
Gerard Deulofeu and Denis Suarez replaced Rakitic and Iniesta as Barcelona looked to hit back, but it was Valencia that were threatening to score the game's second goal approaching the final 15 minutes of action.
Neto had to keep out a smart Luis Suarez effort in the 76th minute, however, and Barcelona finally levelled in the 82nd minute when Alba found the far corner with a super volley after a meeting a pass from Messi.
Andreas Pereira and Zaza both came close to winning it for Valencia in the final moments, but the final whistle went at 1-1 as both teams kept their unbeaten starts intact.
Valencia (4-4-2): Neto; Montoya, Gabriel, Garay (Vezo 86'), Gaya; Soler (89'), Parejo, Kondogbia, Guedes; Zaza, Rodrigo (Pereira 82')
Barcelona (4-1-2-1-2): Ter Stegen; Semedo (Vidal 80'), Umtiti, Vermaelen, Alba; Busquets, Paulinho, Rakitic (Deulofeu 68'), Iniesta (D.Suarez 72'); Messi, Suarez