The capital club kept pace with Barcelona at the top of La Liga by overcoming Miroslav Djukic's side thanks to the Brazil-born forward's double
The capital club were made to work hard for three points against Miroslav Djukic's side, but Diego Costa struck twice either side of a Raul Garcia effort, despite two missed penalties from the Brazil-born forward.
Valencia showed early signs of promise in the match, advancing into Atleti turf, but the the hosts had their first claim for a penalty turned down after just a few minutes, when Costa was felled by Victor Ruiz.
However, netiher side were able to exert their authority on the game and the first half ended up goalless.
Less than 15 minutes after the interval, however, Atleti took the lead. Costa picked up in midfield, drove into the box and fired a shot across Diego Alves.
Getting the breakthrough opened the floodgates and five minutes later, Diego Simeone's side were two goals to the good when Juanfran's cross was miscued into the path of Garcia, who promptly drove home.
Costa was presented with an opportunity to make the points safe shortly afterwards after Victor Ruiz conceded a penalty and though his effort was saved by the keeper, he made amends nine minutes from time by slotting home a second spot-kick.