Sevilla's Vicente Iborra scored the winner for the second game in a row, his strike having decided the derby against Real Betis last week, as he netted on the rebound in the 14th minute after Steven Jovetic's penalty was saved by Gorka Iraizoz.
Earlier, Atletico's Antoine Griezmann struck a brilliant dipping shot to earn a 1-1 draw at Deportivo but the goal was overshadowed by a head injury to team mate Torres who had to be carried off on a stretcher with his neck in a brace.
The late game was billed as a contest between the two leading candidates to take over at Barcelona next season, after Luis Enrique said on Wednesday he would not renew his contract at the champions, and Sevilla's Jorge Sampaoli came out on top.
Ernesto Valverde's Athletic side dominated the game, however, and were unlucky not to draw level before the break when Raul Garcia's diving header struck the post
Sevilla's victory - their fifth in a row in all competitions - leaves them third on 55 points, two behind leaders Barcelona and one adrift of Real Madrid in second with a game in hand.
"We've played a lot of games recently and are feeling the pressure at being near the top, we had won our last four games (before facing Athletic) and we're still fighting at the top. We'll have ups and downs but we're intact," said Sampaoli.
The Argentine coach gave an angry response when asked about the soon to be vacant role at Barcelona.
"I have no idea what you're talking about. I find it incredible people can talk about candidates at this stage in the season, there is no response to that question," he said.
URGENT TREATMENT
Atletico's ex-Spain striker Torres fell face down on the pitch in the 85th minute after challenging for the ball with Depor's Alex Bergantinos and required urgent treatment.
Players from both teams looked concerned as an eerie silence fell over the Riazor stadium while the home fans applauded Torres, who had regained consciousness, as he left the field.
A statement from Atletico said 32-year-old Atletico favourite Torres had suffered head trauma and would spend the night under medical observation in a hospital in Coruna.
"We felt nervous and worried after the awful blow he received," Atletico coach Diego Simeone told a news conference.
"I heard a noise from the bench, I don't know if it was his neck but he felt something. These are awful things that happen in football.
"We are hoping for the best for Fernando, it was a complicated situation for the Deportivo and Atletico players."
Deportivo's former West Bromwich Albion and Real Betis manager Pepe Mel had seen his side take a surprise lead in his first game in charge when Florin Andone pounced on a terrible goal kick from Jan Oblak to score in the 13th minute.
Oblak mis-hit the ball and it was headed towards a surprised Jose Gimenez but Romanian forward Andone was more alert and intercepted before slipping the ball past the keeper.
Atletico's France international Griezmann levelled in the 68th after playing a one-two with Yannick Carrasco and calmly sending the ball spinning at speed over keeper German Lux.
The draw takes Atletico on to 46 points, one point clear of Real Sociedad in the fight for fourth spot after the Basques were held to a 2-2 draw at home to Eibar on Tuesday.
Deportivo are a point above the relegation zone after ending a four-game losing streak which saw Gaizka Garitano sacked.
(Reporting by Richard Martin; Editing by Ken Ferris)
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