- Nahuel Molina (90'+4')
- Yeremy Pino (73')
- Gerard Moreno (90'+7')
Rulli made outstanding saves to prevent three clear goal-scoring opportunities for Atletico, and at least three more key blocks during the game, in which both sides created several chances.
"We saw the game as it was. Very tactical, strategic. They looked to draw us out of our position," Atleti manager Diego Simeone said after the match. "The truth is that although it seemed that they were controlling the game, they didn't have any chances, until the moment when [a] poor clearance which led to their goal.
"It was a tight game. We could have scored through [Yannick] Carrasco, or it could have been 0-2 before it was, with Moreno. We knew that when we play Villarreal. It's always tight and whoever makes a mistake, can lose. We congratulate them and we'll keep working."
After making a strong start to the new LaLiga campaign last Monday with a 3-0 win at Getafe, Atletico were a constant threat in the box with Alvaro Morata and Joao Felix looking ready to pounce.
Morata almost scored a beauty in the first play of the match when he sent a thunderous strike in from inside the area that Rulli stopped with an incredible effort.
Last year's Champions League semifinalists have started the new season where they left off, scoring nine goals combined in their first two LaLiga matches and their UEFA Conference League debut. They forced many mistakes from Atletico's three-man defence on Sunday that also led to good chances.
Jan Oblak made two incredible stops in the first half to keep out long-range strikes from Giovani lo Celso and Etienne Capoue.
Villarreal had a Moreno strike cancelled in the 33rd minute as the striker touched the ball with his right hand when trying to control a rebound in the six-yard-box, after his first effort bounced back off the bar.
In the scorching heat of Madrid both teams slowed down their frantic pace in the second-half, with Villarreal dominating the possession but Atletico creating more opportunities in counter-attacks led by substitute Antoine Griezmann.
Rulli made the stop of the match in the 70th minute when he denied what looked like a certain goal from substitute Matheus Cunha with a one-handed reflex move from close range.
In the very next play, a catastrophic error by Atletico's defender Nahuel Molina when attempting to make a clearance gifted a golden opportunity to Pino who, inside the area, had time to control the ball and roll it into the net past Oblak.
Six minutes later, Rulli made another stunning stop to prevent an equalizer from a Yannick Carrasco close-range header.
Molina's debut in front of his new club's fans was one to forget as he was sent off with a straight red card for a heavy foul on Alex Baena.
With Atletico down to 10 men, Villarreal scored their second in stoppage time through Moreno in a swift counter-attacking move.
Simeone was asked about the possible departure of some of his players, including Morata and Cunha, but after saying on Saturday that he thought the window should close earlier than in does, he said he was happy with the players at his disposal.
"No, I'm about working [on signings], not about asking for things," Simeone said. "We have a very complete squad, let's hope we can keep the same players who are here. If one leaves, let's hope it's because another has arrived. We have a very good squad."
- Ricardo de Burgos Bengoetxea