Two second-half goals - one from the penalty spot - were enough to prevent Diego Simeone's side from closing the gap to Real Madrid and Barcelona
In a game dominated by Celta, Diego Simeone's men struggled to hit the heights of last weekend's 4-0 demolition of Real Madrid and will be particularly unhappy with the award of the penalty converted by Nolito.
Augusto Fernandez clearly handled the ball in the build-up, but the referee played on and Nolito was brought down before getting up to convert the spot-kick himself.
Eduardo Berizzo's side controlled the first half and were well worth a lead that should have been doubled by Joaquin Larrivey.
Either side of that chance, Saul Niguez and Antoine Griezmann forced fine saves from Sergio Alvarez as the game sprung to life, but Atletico conceded again after 71 minutes as the impressive Orellana lashed home to keep the champions seven points behind leaders Real after a first league defeat at Celta since 2005.
Simeone made two changes from the mauling of Real. Saul replaced the injured Koke last weekend and scored so kept his place, with Fernando Torres given the nod to start in place of the suspended Arda Turan.
The hosts did not look like a side that had won just one of their previous 12 league games and Michael Krohn-Dehli flashed a low effort just wide a minute later.
Gustavo Cabral twice saw shots blocked, while Nolito skewed an effort wide from outside the area as Atletico struggled to stamp their authority on proceedings.
The second half started with Celta dominating and they got their rewards, albeit in controversial fashion, after 55 minutes.
Fernandez handled the ball in the centre of the pitch, but nothing was given and in the same move, Nolito was brought down in the area by Mario Suarez.
From the resulting penalty, Nolito made no mistake, sending the goalkeeper the wrong way for his eighth league goal this season.
The champions were almost level a minute later as Saul's rasping drive was parried by Alvarez, who then made a miraculous save to tip away Griezmann's rebound, although the Frenchman was given offside.
It sparked the game into life and Celta should have been out of sight a minute later as Nolito squared to Larrivey, but, with the goal at his mercy, he somehow missed the target.
Back at the other end, Griezmann went agonisingly close to a leveller, but his well-struck shot was blocked by Alvarez, who managed to gather just before the ball crossed the line.
But Celta rounded off a great team performance with 19 minutes remaining when Krohn-Dehli found Orellana in space and he lashed home from inside the area to give Miguel Angel Moya no chance.
Orellana almost notched a second from an almost identical position to his first, but Moya produced a fine low save to divert the ball behind.