Diego Simeone's Atletico had the upper hand for much of the match against a committed Valencia but lacked the sharpness they showed in their 5-1 win over Las Palmas prior to the international break.
In the second half the hosts were generally restricted to set plays, but boss Marcelino can reflect with satisfaction upon a return of five points from a tricky opening to the campaign after an impressive 2-2 draw with Real Madrid in their previous match against Real Madrid.
Atleti, also with one win and two draws in their opening fixtures granted Barcelona an opportunity to claim a healthy early season advantage after their 5-0 win in the Catalan derby on Sunday morning.
The match against Valencia wasn't without its chances with Angel Correa retained in attack for Atletico, powering towards the Valencia penalty area in the fifth minute with his shot scampered by Ezequiel Garay with the ball deflection forcing Neto into an impressive save.
Andreas Pereira, on loan at Valencia from Manchester United had Spain international Juanfran twisting and turning only to blast over from the edge of the box.
Geoffrey Kondogbia was impressive, controlling play during the first half, but Atletico's Correa and Thomas Partey came close to giving the visitors the lead when they seized upon some sloppy work in possession from the former Sevilla man to feed Luciano Vietto, who again overshot .
Chances came quickly after the interval when Neto got behind Yannick Carrasco's well-struck effort before Correa snufferd an opening on the counter-attack with a misplaced pass.
Nico Gaitan was introduced after the hour mark for Correa, making an impact immediately, forcing Neto into making an unconvincing save shortl.
Kevin Gameiro joined fellow substitute Fernando Torres for the final 20 minutes, with the attacking duo enduring similar frustrations and failing to break the deadlock.