Atletico had the better chances in the first period and led at the interval courtesy of a powerful header from Diego Godin.
Costa made up for that miss in the latter stages, however, converting an Adrian Lopez cross from close range to send Atletico clear at the top.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
GETAFE: Codina; Arroyo, Rafa, Alexis, Lago; Mosquera, J.Rodriguez; Castro, Lafita, Leon; Ciprian
ATLETICO: Courtois; Juanfran, Miranda, Godin, Luis; Gabi, Suarez, Koke; Garcia, Costa, Villa
Away end pretty packed and noisy 15 mins before Getafe v Atlerico kicks off : pic.twitter.com/tSSJ3VgzQo— Dermot Corrigan (@dermotmcorrigan) April 13, 2014
8 - Getafe are currently on their worst ever winless top-flight home run, eight games (D4 L4). Depression.— OptaJose (@OptaJose) April 13, 2014
3 - Diego Costa has missed a joint-high three penalties in La Liga this season, along with Ivan Rakitic. Erratic— OptaJose (@OptaJose) April 13, 2014