Diego Simeone's men welcomed Celta to the Wanda Metropolitano after a 2-0 defeat to Barcelona that effectively ended its title hopes.
Diego Costa received an eight-match ban for insulting the referee during that game, and Atletico was often second best against a resurgent Celta, who had taken seven points from its last three matches to boost hopes of survival.
However, Griezmann lashed home a 42nd-minute free-kick and Morata doubled their lead 16 minutes from time as Atletico increased their lead over Real Madrid - which plays Leganes on Tuesday (NZST) - to five points in the battle for second. Celta remains two points above the drop zone.
Atletico struggled to create much in the early going and owed much to Jan Oblak for keeping them level. The Slovenia international produced a reaction save to keep out Maxi Gomez's deflected effort and then made an even more impressive stop from Ryad Boudebouz's bicycle kick follow-up.
Opposite number Ruben Blanco did well to get a touch to Juanfran's low cross and take it away from numerous Atletico players queuing up to meet it in the box, but Oblak continued to be the busier of the two goalkeepers.
He was again required to preserve parity when he dove to his left to deny Sofiane Boufal after the Frenchman met Boudebouz's lay-off first time.
Celta was made to pay for not capitalising on its superiority as Griezmann powered a free-kick into the top-left corner after Vitolo was fouled by Gustavo Cabral.
Chances were less frequent in the second half but Morata made the points safe when he rounded Blanco after being played through on goal by Griezmann.