Without suspended Italy striker Giuseppe Rossi, Villarreal lacked their usual bite in attack and substitute Juan Albin snatched the winner for Getafe in the 89th minute after their defender, Daniel Diaz, had been sent off just before halftime.
Uruguayan midfielder Albin, whose low shot squirmed just inside the post, was also dismissed as he celebrated the goal by removing his shirt and was shown a second yellow card.
Depor goalkeeper Daniel Aranzubia saved Diego Forlan's fifth-minute penalty before Aguero, whom local media reported on Saturday had agreed a contract extension, struck twice before halftime to lift Atletico to sixth spot.
Sevilla striker Frederic Kanoute had a first-half penalty saved as the Andalusians' poor run continued when they lost 3-1 at home to lowly Almeria in the regional derby.
The Mali international pulled a goal back to make it 2-1 in the 83rd before Almeria's Pablo Piatti scored his second of the night to condemn Sevilla to a fourth straight defeat, prompting disgruntled whistling at the Sanchez Pizjuan stadium.
The referee brandished a straight red card at the Argentine defender after he cut down Villarreal's pacy Brazilian striker Nilmar in full flight.
The numerical advantage immediately lifted the visitors. Nilmar burst clear moments before the break but his low shot was well saved by Jordi Codina's outstretched leg.
Villarreal's Spain midfielder Santi Cazorla and former international Marcos Senna saw plenty of the ball but were unable to unlock a determined home defence and Francisco Casquero's header set up Albin to snatch the win.
Almeria goalkeeper Diego Alves was on inspired form in Sevilla and parried Kanoute's spot-kick after the referee ruled Fabian Vargas had handled in the area.
But a miserable night for Sevilla, missing the injured Luis Fabiano and Jesus Navas, was complete when defender Alexis Ruano was shown a second yellow and Piatti grabbed Almeria's third goal moments later with a clever backheel.
