The game started slowly but burst into life on the 28 minute mark after Costa received his first red card since January 6 2018.
Jose Gimenez and Diego Godin were both booked before several players from both sides got involved with the referee.
Costa then questioned the decision before he was dismissed for alleged foul and abusive language.
As Costa left the pitch he was approached by Gerard Pique, and the pair subsequently clashed.
Pique grabbed the face of his opponent who brushed off his rival, before the situation seemed to calm down.
Costa walked down the tunnel and Pique returned to the action, with the comments of the latter seem to calm his ex-international team-mate down.
The former Chelsea striker has endured a torrid season in front of goal, scoring just once in 14 league appearances.
Despite that poor form, Diego Simeone revealed earlier this week that he trusts the forward “until death”.
“I trust Diego Costa until death and I hope he stays next year,” Simeone said.
“I have complete confidence in him, he is a hugely important player for us and it is no coincidence that we have started winning trophies again since his return.
“We can only take this game by game, we do not look further ahead than the next game.”