Correa's thunderbolt has seen Atletico cut the gap on league leaders Barcelona to nine points, while Valencia remain in third position - one point ahead of fourth-placed Real Madrid.
Koke had the first real attempt of the match in the 11th minute, but the midfielder's effort was always wide of the Valencia post as the early exchanges passed without any major incidents.
Atletico were the team pressing forward as the first period passed its 30-minute mark, although opportunities were few and far between as Gabriel Paulista and Ezequiel Garay combined to tame Diego Costa.
Costa did have a super chance to send Atletico ahead 10 minutes before the break, but the centre-back saw his powerful header saved by the brilliant Neto, before Saul missed the crossbar with an effort moments later.
Valencia's clearest chance of the first period arrived in the latter stages when Dani Parejo picked out Simone Zaza with a cross, although the striker's effort never really threatened to find the back of the net.
Atletico lost Stefan Savic to injury in the first half, and then lost their second starting centre-back Diego Godin in the 49th minute following a sickening collision with Neto, which might well have seen the Uruguay international loose some teeth.
Godin's replacement Juanfran curled over the Valencia crossbar just before the hour, but Atletico took the lead moments later when Correa picked out the top corner with a stunning strike from the edge of the box.
Atletico had the ball in the back of the Valencia net for the second time in the 64th minute, but Griezmann's effort was ruled out due to Costa fouling Neto in the build-up.
Neto then kept out a Correa effort in the 73rd minute as Atletico attempted to put the game to bed. In the end, one goal proved to be enough to secure all the points as Valencia ended the night without managing a single shot on target.
ATLETICO (4-4-2): Oblak; Vrsaljko, Savic (Gimenez 29'), Godin (Juanfran 51'), Lucas; Correa, Koke, Saul, Carrasco (Gabi 61'); Griezmann, Costa
VALENCIA (4-4-2): Neto; Vezo, Paulista, Garay, Gaya; Maksimovic (Soler 65'), Parejo, Kondogbia, Lato (Rodrigo 62'); Mina, Zaza