The Croat stabbed home from close range just before the break to settle the capital clash, with the hosts finishing the game with 10 men
Atletico Madrid made the most of Barcelona's El Clasico humbling by beating Getafe 1-0 to move within two points of the La Liga pacesetters.
The reigning champions made the short trip across Madrid on Sunday and rarely looked troubled by their neighbours, claiming a victory to capitalise on Barca's 3-1 loss at Real Madrid 24 hours earlier.
Mario Mandzukic netted from close range five minutes before the break to send Atletico on their way, but things should have been far more comfortable as they spurned numerous opportunities in the first half.
And after starting the second half encouragingly, Getafe handed Atletico a numerical advantage when captain Alexis earned a red card for striking Mandzukic in the face.
Despite finding themselves with an extra man, Diego Simeone's side seemed reluctant to throw players forward in search of a second goal that would have killed the game.
To their credit, Getafe attacked valiantly in search of an equaliser even though they were a man down, but Atletico's typically resilient defence held firm to seal all three points for the visitors.
Getafe coach Cosmin Contra acknowledged pre-game that the champions would have to have a bad day if he was to outsmart his former Atletico team-mate Simeone in the opposing dugout.
And it looked clear from the early exchanges that it would be a long evening for Getafe, as Atletico dictated the tempo right from the start and saw a penalty claim rejected in the 12th minute.
Guilherme Siqueira charged forward from left-back to great effect but, although he appeared to be tripped by Emiliano Velazquez, referee Mario Melero refused to point to the spot.
Vicente Guaita failed to hold on to Antoine Griezmann's half-volley, and Mandzukic stabbed home from close range after Arda Turan inadvertently knocked the initial rebound to the Croatian.
Getafe began the second half with renewed optimism, though, and only the heroics of their former goalkeeper Miguel Angel Moya in the Atletico net stopped them from restoring parity.
The 30-year-old first swatted away Naldo's flicked effort, before palming away goal-bound attempts from Alexis and Angel Lafita in quick succession.
However, the hosts' hopes of drawing level suffered a significant blow in the 56th minute as their skipper Alexis received a straight red for striking Mandzukic on the side of his face, with tempers flaring on both teams.
Despite going down to 10 men, Getafe continued to press for an equaliser and substitute Baba Diawara went close just a few moments after coming on, sending a half-volley just wide from 25 yards.
But Atletico successfully repelled Getafe's spirited late efforts to find a leveller, meaning they could make the short journey home with a valuable victory under their belt.