Diego Simeone's men welcomed Celta to the Wanda Metropolitano following a 2-0 defeat to Barcelona that effectively ended their title hopes.
Diego Costa received an eight-match ban for insulting the referee during that game, and Atletico were often second best against a resurgent Celta, who had taken seven points from their 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 - who play Leganes on Monday - to five points in the battle for second. Celta remain two points above the drop zone.
Atletico struggled to create much in the early going and were grateful 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 were made to pay for not capitalising on their 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.
What does it mean? Griezmann lifts under-par Atleti
Atleti may have bounced back from their Camp Nou disappointment, but this was another game where they underperformed, with such displays far too common in a season where they had a clear opportunity to dethrone Barca.
As so often is the case, it was Griezmann who hauled them into a winning position. His free-kick was unstoppable and his throughball for Morata to wrap things up perfectly weighted.
Oblak shows his class
Oblak is seen as perhaps the best goalkeeper in the world, and he showed why with three excellent saves to keep Celta at bay.
Mor needed from Emre
While Celta's forward line generally caused Atletico problems, Emre Mor struggled to make an impact. He had no shots, created no chances, and conceded three fouls before being taken off in the 65th minute.
Key Opta Facts:
- Only Barcelona's Lionel Messi (six from 38 attempts) has scored more direct free-kick goals than Griezmann (three from 11) in LaLiga this season.
- Griezmann has scored 20 or more goals in each of his five seasons for Atletico Madrid in all competitions (20 goals in 2018-19).
- He has also produced nine assists in LaLiga this season, equalling his best tally in a single top-flight campaign (nine in 2017-18).
- Atletico have kept more clean sheets than any other side in the top five European leagues this season (18).
- Morata has scored five goals in his last seven LaLiga matches for Atletico.