Diego Simeone's side appeared to be in complete control at El Molinon on Saturday after Antoine Griezmann's stunning free-kick had given them the lead in the 29th minute.
Atletico – who needed penalties to beat PSV in the Champions League on Tuesday – soaked up plenty of Sporting pressure but were unable to hold on as goals from Antonio Sanabria and Carlos Castro handed the relegation-threatened hosts a much-needed victory.
The defeat could see Atletico fall 11 points behind league leaders Barcelona should the latter beat Villarreal on Sunday, while Real Madrid could move to within one point of their city rivals with victory over Sevilla.
But despite admitting the situation has become harder, Koke is refusing to throw in the towel yet, telling reporters: "We were fully prepared to play two games in a week, we had held up well. .
"[But] we have thrown away three very important points in the fight for the title. It makes it very difficult for us. We are still in contention. Barcelona face a very tough match against Villarreal."
Atletico's day went from bad to worse with the news defender Jose Maria Gimenez suffered a hamstring injury during the defeat.
No timescale has been put on his return, but the latest setback will be a particular blow to Simeone who is already without Diego Godin with a similar problem.