Talismanic striker Costa scored the second on Sunday to re-establish a three-point lead over city rivals Real at the summit, but he paid the price for his bravery in sliding home from close range to wrap up the victory.
The 25-year-old - who has only just returned from a hamstring strain - collided with the post in the act of scoring, appearing to take a heavy blow to his leg, and was carried off on a stretcher in clear discomfort.
Costa's goal came after he had already missed from the penalty spot, with Angel Lafita's red card compounding a difficult game for Cosmin Contra's relegation-threatened Getafe side.
Following the victory against Gerardo Martino's Barca, Simeone had demanded full focus from his side - but despite that, Atletico seemed lacklustre in the early stages.
Alexis almost put the hosts ahead in the 19th minute, only to head Pedro Leon's corner agonisingly wide.
After 28 minutes, Godin spurned a glorious chance as he rose to meet Koke's right-wing free-kick but nodded the ball straight at Jordi Codina in the Getafe goal.
The Uruguayan out-jumped Roberto Lago at the back post in the 40th minute, looping a powerful headed effort over Codina following Juanfran's lofted cross-field pass.
Getafe started the second half with renewed determination and they were almost rewarded with an equaliser, but the unmarked Juan Rodriguez could only head Leon's right-wing cross straight at Thibaut Courtois before the home side were the architects of their own downfall in the 64th minute.
The frustrated Costa finally doubled Atletico's lead in the 84th minute, as he tapped Adrian Lopez's pass in at the back post, but the Spain international suffered a nasty leg injury as he collided with the frame of the goal, with a gash visible just below his knee as he received treatment.
