Unai Emery's men opened their season with an impressive 3-0 win at Real Valladolid last weekend but the scalp of Atletico will raise hopes of a possible challenge for Champions League qualification.
The result was a reality check for the capital side, though, who had also started the campaign with a 3-0 success at Getafe.
Villarreal, who reached last season's Champions League semifinals, are one of four teams with two wins from two matches and edged above reigning champions Real Madrid on goal difference.
The away side made a fast start at the Estadio Metropolitano, with Atletico goalkeeper Jan Oblak forced into fine saves from Giovani Lo Celso and Etienne Capoue.
Moreno thought he had given Villarreal a halftime lead, but his effort was ruled out for a handball.
Matheus Cunha was introduced midway through the second period by home coach Diego Simeone in place of Alvaro Morata and almost broke the deadlock in the 72nd minute, only to be denied by keeper Geronimo Rulli.
Teenage winger Pino instead put Villarreal in front just a minute later, capitalising on a poor clearance to drill a fine low shot into the bottom corner.
Atletico's Nahuel Molina was sent off deep into injury-time and Moreno netted in the 97th minute to send Villarreal top.