The Spain striker volleyed home spectacularly in the first half before the Paraguayan slotted home in injury time to hand Diego Simeone's side its first defeat of the campaign
In a match of few clear-cut chances, it took a moment of brilliance from the Spain striker to settle the matter, as he allowed Adil Ramis' long ball to drop over his shoulder before volleying into the far corner, leaving Thibault Courtois helpless between the posts.
Atletico responded and applied pressure throughout the second half but it was unable to make much headway in front of goal, and Valencia settled matters late on as Sofiane Feghouli played in Valdez to slot past Courtois and seal the points.
It was a game billed as a match up of two of the main pretenders to the Liga crown, featuring a fearsome battle of the number nines, as Soldado and Radamel Falcao vied for supremacy in front of goal.
The visitors were targeting a ninth victory from their opening ten matches in La Liga this season, which would have seen them better their start to their famous double-winning campaign of 1996, while the hosts were keen kick on up the table after recovering their form of late.
Atletico started proceedings brightly, with Falcao coming close with a range-finding free kick in the opening 15 minutes while Che keeper Diego Alves was forced into a couple of important punches from corners.
However, in a half bereft of clear-cut chances, it was Valencia's number nine who struck the first blow shortly before the half hour mark. Adil Ramis floated a superb long ball over the top of the Atleti defence, and Soldado watched it drop over his shoulder before volleying superbly across goal and into the far corner.
The match wound down somewhat towards the interval, but not before Manuel Pellegrini was sent to the stands after an exchange with the fourth official on the touchlines, as the tension of the match threatened to reach boiling point shortly before the break.
The second half followed a similar pattern to the first, as both sides struggled to create many meaningful chances.
Arda Turan came close after some clever interplay on the edge of the box but could only find the side netting, whilst Alves was called upon to punch an Emre free kick off the line.
Valencia seemed content to sit off and wait to launch a counterattack, with Andres Guardado coming close with a low drive from 20 yards.
Turan - Atletico's brightest player - hit a fearsome dipping effort which had Alves concerned, but the Turkey international was not able to find a way past the Brazilian stopper.
Valencia continued to frustrate the visitors, with the excellent combination of Ramis and Victor Ruiz consistently frustrating the efforts of Falcao and Adrian Lopez up front as Atleti surprisingly struggled to create any real chance of note in the second period.
With Simeone's charges desperately seeking that elusive equalizer, Valencia was always likely to get the chance to settle matters on the counter and, in the dying moments, Haedo Valdez did just that. Some superb control and a sliderule reverse pass from Sofiane Feghouli allowed Valdez to race clear on goal, and after a clever dummy sent him past Courtois, he slotted home into the unguarded net to seal the points for the hosts.
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