Costa had been a doubt in the Atletico ranks after struggling with injuries in recent weeks before finally being confirmed in the starting line-up to play the tie.
But after less than 10 minutes the volatile ex-Chelsea man found himself in the referee's book as Atletico's clash with Juve started in a predictably fractious manner.
Team-mate Jose Maria Gimenez handed Cristiano Ronaldo the chance to score from a long-range free-kick early on after felling the striker eight minutes in.
Ronaldo's efforts to take the kick were then delayed by Costa, who was seen inching forward in the wall in a bid to narrow the Portuguese's angle on goal.
The subsequent decision to hand Costa a booking provoked a fierce reaction in the Atletico ranks, further raising the heat in the Wanda Metropolitano.
Ronaldo did not disappoint when eventually cleared to take aim, forcing Jan Oblak to make a spectacular flying save in the tie's first real chance.
Atletico coach Diego Simeone will now have to shuffle his hand ahead of the second leg, which will take place in Turin on March 12.
Alvaro Morata, a former Juve player himself, would be the logical choice to replace Costa against his old club, while Angel Correa could also feature alongside first-choice forward Antoine Griezmann.
The Madrid side will also be without Thomas Partey, who was booked in the final minutes of the first half for a clumsy tackle on Paulo Dybala to rule himself out of contention.
Costa's start was his first since December and only his second appearance in that time span.
It was also his fourth Champions League appearance of the campaign, with the Spanish international scoring one goal: the opening finish of a 2-1 victory over Monaco in Atleti's first match of the group stage.
He's featured 12 times in the league as well with one goal to his name as well as two finishes in the UEFA Super Cup.
Atletico's next match will be in the league as the club will take on Villarreal on Sunday.