Atletico boss Diego Simeone made five changes to the team that started against Lokomotiv Moscow in the Europa League on Thursday night, with Jan Oblak, Sime Vrsaljko, Diego Godin, Gabi and Vitolo all coming into the XI.
As for Celta, head coach Juan Carlos Unzue named the same side that started last weekend's 2-1 win over Las Palmas, meaning that Emre Mor kept his spot alongside Iago Aspas and Maxi Lopez in the final third of the field.
Vrsaljko's energy down the right proved a key feature of Atletico's work inside the opening 25 minutes, but neither goalkeeper had a save to make during a tight start to the match, with both teams struggling to create openings.
Godin had Atletico's first serious opportunity of the match when he met a Koke corner just before the 30-minute mark, but the centre-back's header dropped just wide of the post.
Celta's best chance of the first period fell to Sergi Gomez in the 32nd minute, but the defender saw his close-range strike deflected wide of the post by the diving Godin, before Pablo Hernandez and Aspas both had half-chances for the visitors.
It was Atletico that took the lead on the stroke of the interval, however, with Griezmann showing incredible calmness inside the Celta box to pick out the top corner after dancing past Jonny inside the box.
The visitors had a huge penalty shout early in the second period when Maxi Gomez went down under a challenge from Lucas Hernandez, but the referee was not interested.
Celta had a golden chance to level the scores in the 55th minute when Mor picked out Nemanja Radoja with a brilliant cross, but the midfielder saw his effort strike the post.
Less than two minutes later, Atletico doubled their advantage with Vitolo producing a wonderful chip past Blanco after Griezmann had released the former Sevilla winger inside the Celta box.
The home side then had their third in the 63rd minute when substitute Angel Correa worked some space inside the Celta box before finding the bottom corner with a smart finish.
Both managers made three changes in the period that followed, which saw the tempo drop in the Spanish capital.
Fernando Torres and Kevin Gameiro would have been keen to get among the goals in the latter stages of the contest, but it was Celta that came closest to scoring in the final 10 minutes, with Maxi Lopez testing Oblak from distance.
ATLETICO MADRID (4-4-2): Oblak; Vrsaljko, Gimenez, Godin, Lucas; Koke, Saul, Gabi, Vitolo (Correa 59'); Griezmann (Gameiro 69'), Costa (Torres 80')
CELTA VIGO (4-3-3): Ruben; Mallo, S. Gomez (Cabral 77'), Roncaglia, Jonny; Lobotka, Radoja (Brais 67'), Hernandez; Aspas (Boye 72'), M. Gomez, Mor