Atletico’s transfer ban ended last week and Costa was playing his first league game since rejoining the Spanish club from Chelsea.
The 2-0 win, in which France star Antoine Griezmann set up the opener for Angel Correa on 18 minutes, lifts Atletico into second, six points behind Barcelona who play Levante on Sunday.
It also took Atletico five points clear of third placed Valencia.
Costa had been lively the whole match and received a yellow card for a foul in the 62nd minute. Five minutes later he met a low cross to put his side 2-0 up and immediately earned a second yellow for leaping into the stands to celebrate with fans.
The brooding striker looked totally perplexed by the decision but his boderline style of play may inject some much needed bite to the Atletico forward line.
Diego Simeone’s side looked as hard to beat as ever — with just eight goals conceded and one defeat in 18 league games — but they have scored only 27 with Greizmann struggling to find the net, hitting just five league goals so far.
Atletico haven’t won La Liga since Costa left for London, where he won two Premier League titles in three years after rifling the Madrid club to their tenth league championship with 27 goals.