An uncharacteristically error-strewn performance from Diego Simeone’s men was deservedly punished by the visitors, who could have been out of sight before the goal but for two fine saves by Miguel Angel Moya.
Defeat leaves Atletico now seven points adrift of leaders Real Madrid and still three off second-placed Barcelona, who were the last team to beat Atletico on home soil in La Liga back in May 2013, whilst Villarreal move up to sixth.
Atletico were playing for the first time at the Calderon since a Deportivo La Coruna fan was killed in clashes near the stadium ahead of a meeting between the two sides a fortnight ago.
The club had promised to crackdown on their unruly ultras, but the unusually flat atmosphere in front of a half-empty stadium seemed to affect the Spanish champions in a first-half littered with errors.
Koke sent a rasping shot just wide from distance, but a promising start by Atletico quickly petered out and it took until seven minutes before half-time for the first shot on target as Tiago stung the palms of Sergio Asenjo.
Villarreal then had a glorious chance to open the scoring a minute before the break when Denis Cheryshev burst clear but opted to go for goal himself rather than square to the unmarked Vietto and Moya made a comfortable save.
The visitors were then furious with the referee moments later when Atletico captain Gabi appeared to handle inside the area, but Pedro Jesus Perez Montero remained unmoved.
Vietto fired inches wide from the edge of the area as Villarreal also began the second period brightly, but that effort appeared to wake Atletico from their slumber.
Mario Mandzukic had a wonderful chance to continue his fine goalscoring form when he latched onto Diego Godin’s knockdown, but former Atletico ‘keeper Asenjo bravely blocked the Croatian’s effort from point black range.
Moments later Mandzukic was denied by Perez Montero as he harshly ruled out the former Bayern Munich man’s headed finish for a push on Mario Gaspar.
– Left exposed –
In their push for a winner, though, Atletico were leaving themselves exposed on the counter and were only pardoned by a poor touch from Vietto when he was this time released clean through on goal by Cheryshev.
The Argentine’s mis-control allowed Moya to get a vital touch before Diego Godin completed the clearance.
Godin then snatched at the type of headed opportunity he normally converts at the other end from Koke’s pinpoint cross and Tiago fired wide after good link-up play by Mandzukic.
Atletico were thankful to another fine stop from Moya to prevent Cheryshev opening the scoring with a piledriver from a narrow angle.
Yet, there was nothing he could do to prevent Vietto inflicting a first league defeat at home in 19 months when he turned Godin and fired high into the net six minutes from time.
Earlier, Sevilla’s hopes of securing a return to the Champions League next season suffered a blow as they were held 0-0 at home by a resilient Eibar at the Sanchez Pizjuan.
The hosts dominated in terms of possession and shots on goal, but only forced Eibar ‘keeper Xabi Irrureta into two saves either side of half-time through Ever Banega and Kevin Gameiro.
Indeed, it could have been even worse for Unai Emery’s men had Beto not produced a fine double save of his own to deny Derek Boateng and Federico Piovaccari five minutes before the break.
A point means Sevilla remain in fourth, but are now only two points in front of Valencia, whilst Eibar move up to ninth.
On Saturday, Barcelona’s title hopes suffered a blow as they fell four points behind Real Madrid after being held to a disappointing 0-0 draw at Getafe.
Twenty-four hours earlier, two late Cristiano Ronaldo goals had helped Real make it 20 consecutive victories in all competitions as they saw off Almeria 4-1- AFP