Atletico Madrid stunned Juventus 2-0 in the first-leg of their Champions League round 16 tie.
Diego Simeone's side were denied a penalty and an Alvaro Morata goal by the video assistant referee before they opened the scoring.
Jose Maria Gimenez pounced from eight yards after Morata's header was blocked by Mario Mandzukic.
Diego Godin netted a half-volley, via a deflection off Cristiano Ronaldo.
Striker Costa and midfielder Thomas Partey of Atletico Madrid and Juve left-back Alex Sandro will all miss the second leg on Tuesday, 12 March after picking up their third bookings of the tournament.
Ronaldo - who is aiming to win a sixth Champions League and a fourth in a row - had Juve's best chance as his powerful 35-yard free-kick was tipped over by Jan Oblak.