Atletico struggled in the derby clash against 18th place Rayo but eventually snatched a late victory to move second in the table, four points behind leaders Barcelona, who host Real Valladolid later on Saturday.
Rayo had the better of the first half with Adrian Embarba going close, while Atletico goalkeeper Jan Oblak denied Raul de Tomas early in the second half.
Atletico broke the deadlock in the 74th minute at Vallecas when Alvaro Morata teed up Griezmann and his close-range volley deflected past Stole Dimitrievski.
"We know that here in Vallecas they press you a lot, they are a good team, the size of the pitch is difficult," said Atletico forward Diego Costa, who made his return from injury as a substitute.
"It was important to win the game after two defeats, we won here against a good team that will surely stay up."
(Reporting by Rik Sharma; Editing by Toby Davis)
