A battle between the two best defences in La Liga was unsurprisingly settled by a single goal when the Italian turned home Cedric Bakambu's cross eight minutes from time.
Victory hauls Villarreal to within five points of fourth-placed Sevilla, who have a game in hand, and eight of Atletico in third.
Atletico enjoyed the vast majority of the play and chances, but were undone by a brilliant performance by Andres Fernandez in the Villarreal goal.
"We played well and went looking for the goal the whole game but the ball didn't want to go in."
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Fernandez made a stunning double save early on as Angel Correa wriggled free inside the area to fire goalwards before Saul Niguez's powerful header was turned to safety.
The Villarreal stopper also denied the on-form Antoine Griezmann and Nico Gaitan before the break.
Gaitan then had Atletico's best chance of the game early in the second-half. However, he failed to reward boss Diego Simeone for a rare start as again he was denied by Fernandez's outstretched hand.
Soriano should have done better with a huge chance that was blocked by Diego Godin 12 minutes from time.
However, he made amends just four minutes later by turning home Bakambu's cross to inflict just Atletico's second league defeat since the sides last met back in December.
And Atletico were also dealt a blow a week ahead of the first leg of their Champions League semi-final with Real Madrid as Belgian winger Yannick Carrasco had to be replaced just 15 minutes after coming on as a substitute with a collarbone injury.
Defeat means Granada could now be relegated as early as Saturday should they fail to win at Real Sociedad and Leganes beat Las Palmas on Wednesday.
Adams's men remain seven points adrift of safety and have yet to even score since he replaced the sacked Lucas Alcaraz earlier this month.
Former Barcelona winger Ramirez produced the few true moments of quality with a rasping drive from outside the area two minutes into the second-half before sealing the victory in stoppage time with his fifth goal in as many games.
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