Australia goalkeeper Mat Ryan kept a clean sheet on his La Liga debut as UEFA Champions League hopeful Valencia was held to a disappointing goalless draw at Rayo Vallecano.
Ryan made his competitive debut for Valencia in its 3-1 Champions League win over Monaco in midweek, and followed that up by going unbeaten on his league debut.
Valencia had the better of the first half and came within inches of grabbing an injury-time winner when former Rayo striker Alvaro Negredo's powerful effort was tipped away by the excellent Tono.
Rayo Vallecano made a typically intense start to the game but Valencia looked dangerous every time it came forward on the counter-attack.
Rodrigo de Paul was denied by Tono's legs after being played in by Negredo, and the stopper had to reach out again a few minutes later to punch away a shot from Santi Mina, while later in the half Pablo Piatti skewed wide.
Rayo had few openings in the first half, with debutant Patrick Ebert forcing a save from Ryan and Manucho denied a clear shot at goal due to a vital tackle by Shkodran Mustafi.
Paco Jemez's side was more dangerous in the second half and squandered two golden chances to take an unlikely lead. Manucho arrived at the far post unchallenged ready to meet a low cross but slipped just as he was about to pull the trigger, and then Ebert narrowly failed to connect with another low cross from the right.
Rayo's good work was almost undone at the death by former Vallecas favourite Negredo, but Tono was again up to the task.
A first-half goal from Antoine Griezmann ensured that Atletico Madrid made a winning start to the new season as it defeated Las Palmas 1-0 at the Vicente Calderon.
Diego Simeone handed a debut to new recruit Jackson Martinez, but the Colombia international struggled to threaten the goal in almost an hour on the pitch.
Instead it was left to one of last season's leading lights, Griezmann, to settle the contest, though there was a large element of luck as the France international's deflected effort secured three points.
The result capped a positive week for Atletico which also saw key defender Diego Godin sign a one-year contract extension.
However, Simeone will have concerns about his side's inability to kill the game off, with Las Palmas seeing a string of late chances repelled by the excellent Jan Oblak in Atleti's goal.
Expected to dominate against newly-promoted opposition, Atleti created two chances in the opening five minutes.
First, Griezmann flashed a snap-shot narrowly wide before Tiago climbed highest to meet a Juanfran cross from the right, but failed to direct his header on target.
An opening goal for the host seemed inevitable as it continued to pile on the pressure and it duly arrived in the 16th minute when Griezmann's 22-yard free-kick deflected off the wall and left Las Palmas goalkeeper Raul Lizoain flatfooted.
Las Palmas refused to crumble after that early setback and although an off-target, long-range effort from Roque Mesa was all it could manage going forward, it defended stoutly, with Lizoain producing a fine save to deny the lively Griezmann in first-half stoppage-time.
Returning left-back Filipe Luis had been a constant threat for Atleti during the opening period and he continued to torment the Las Palmas defence after the break, whipping in a superb cross on 55 minutes which the onrushing Martinez was just unable to slide into the net.
The Brazil international neglected his defensive duties moments later, however, failing to mark David Simon at a set-piece and allowing the defender a free header which grazed the crossbar as the visitor gathered momentum.
And Simeone's men enjoyed another let-off in the 74th minute when Oblak pulled off a magnificent save low to his right to keep out a close-range effort from Aythami.
The altogether busier Lizoain then matched Oblak at the other end by keeping out a ferocious angled strike from Filipe as Atleti continued to press for a second goal right to the final whistle, while Koke clipped the post with a free-kick in the final minute of normal time.
Next up for the side from the capital is a tricky trip to Sevilla, while Las Palmas will hope to pick up its first points of the season when it hosts Levante.
Espanyol also got off the mark with a win on the opening day, with Salva Sevilla's early goal enough for a 1-0 win over Getafe.
Santiago Vergini was sent off on his debut for Getafe, which was unable to capitalise on an Espanyol side which lost of a number of key players over the northern summer.
Sevilla got the host under way with less than three minutes on the clock, lifting a free-kick over the wall and in off the post.
The Catalan side failed to double its advantage, however, while Pedro Leon went close for Getafe shortly after.
After he was booked early in the second half, Vergini was shown a second yellow with over 10 minutes to go, allowing Espanyol to hold on to claim victory.
David Moyes's Real Sociedad was held to a goalless draw away at Deportivo La Coruna, despite dominating much of the first half.
Northern summer signing Jonathan de Jesus went close for Sociedad, with his ambitious bicycle-kick drifting wide, before seeing an effort well saved by Deportivo keeper German Lux when through one-on-one.
The home side could have taken the lead in the second half but Lucas Perez saw the flag raised for offside after a set-piece routine.
Fede Cartabia was prominent in an improved showing after the break, hitting the side-netting from a free-kick.
Geronimo Rulli reacted well in the Sociedad goal to tip another set-piece over the bar as Moyes's side held on in the second period to start its campaign with a point.