Turkish international star Arda Turan did not start against his former side but did play the last 20 minutes replacing his Rakitic.
Atleti actually took the lead when Griezman put the away side ahead but Messi equalised on the half an hour mark and Luis Suarez put Barcelona ahead just eight minutes later.
The away side were dealt a further blow when Filipe Luis was sent off and Godin made matters worse when he was shown a red card just after half time.
Turan completed 30 passes with a 93 percent accuracy and almost scored against his former side soon after coming on but his shot went narrowly wide.
Barcelona have now won all eight games since Turan made his debut against Espanyol at the start of the month. The reigning La Liga champions have scored 22 goals and conceded just four goals since he made his first start.
Barcelona – Atletico Madrid
Stadium: Camp Nou
Kick-Off: 15:00 GMT
Barcelona Starting Line-up (4-3-3): 13.Bravo 3.Piqué 4.Rakitic 5.Sergio 6.Alves 8.Iniesta 9.Suárez 10.Messi 11.Neymar Jr 14.Mascherano 18.Jordi Alba
Subs: 1. Ter Stegen 7. Arda Turan 17. Munir 20. Sergi Roberto 22. Aleix Vida l23. Vermaelen 24. Mathieu
Manager: Luis Enrique
Atlético Madrid Starting Line-up (4-4-2): Oblak, Juanfran, Godín, Giménez, Filipe Luis; Gabi, Augusto, Koke, Saúl, Carrasco and Griezmann
Manager: Diego Simeone
Goals: 10′ Koke, 30′ Messi, 38′ Suarez