The striker had been unable to play for Diego Simeone's side until now due to the club's transfer embargo, but he was named on the bench for Atletico's clash against second division side Lleida.
That was Costa's first competitive goal for Atletico since he scored a penalty in their 3-1 victory over Chelsea in the Champions League back in April 2014. "It was very important for me", said Costa.
Copa Del Rey: Diego Costa scores on Atletico debut against Lleida
Vietto is under contract with Atletico until June 2021, but a good spell at the Mestalla outfit could trigger an anticipated exit for a player that was never able to respond to the expectations around him.
Simeone is hoping that the 29-year-old Costa is still the same caliber as when he scored 20 goals to lead Chelsea to the EPL title.
"His departure annoys me because his play hasn't been accompanied by goals at a team which doesn't wait".
The Brazil-born Spain global appeared to hurt his right knee in scoring, and received lengthy treatment on the sidelines, although he played on to see another sub, Antoine Griezmann, finished the scoring with a deflected free kick in added time.
Costa's goal comes 99 days after Blues agreed to sell the sulking striker back to his former club for in a £67million deal, with Atletico shelling out £60m up front. "The team did well in a tough game, which is what makes me happiest".
Antonio Conte told Costa by text message that he was not in his plans at the end of last season.