Ivan Rakitic had sent Barcelona, who remain third in the table, into a 41st-minute lead, but Atletico levelled just past the hour through Angel Correa as Diego Simeone's side continued their unbeaten start.
Luis Enrique selected his tried-and-trusted XI at Camp Nou, with Andres Iniesta and Javier Mascherano both handed starts, while it was Lionel Messi, Luis Suarez and Neymar in the final third of the field.
As expected, it was the home side that dominated possession inside the opening 10 minutes, but aside from a weak header from Rakitic, which fell for Jan Oblak, Atletico were allowed a comfortable start.
It took until the 15th minute for Barcelona to register a proper attempt on target and that came from Messi, whose powerful strike from the edge of the box was saved by Oblak. Down the other end, Marc-Andre ter Stegen was forced into action to keep out a curling effort from Carrasco as both sides had decent chances to make the breakthrough.
Barcelona continued to dominate the possession as the first period gathered pace, although Atletico were always a threat on the counter-attack, and Carrasco fired another strike wide of Ter Stegen's post on the 30-minute mark. Neymar was next to come close for the hosts after the ball fell for the Brazilian outside the box, but his curling effort missed the post.
The home side would not take no for an answer, however, and took the lead in the 41st minute when Rakitic headed a Iniesta cross into the bottom corner from inside the box.
Atletico almost equalised straight from kickoff when Griezmann drove through the heart of the Barcelona midfield before striking towards goal, but Ter Stegen was on hand to make the save.
There was hardly time to take a breath at the start of the second period as the match flowed from end to end, and Griezmann again had a shot from distance in the 49th minute, but this time the Frenchman cleared the home side's goal.
Barcelona were forced to make a change just before the hour when Messi over-stretched his groin, and it was former Atletico midfielder Arda Turan that replaced the Argentine, who limped off the field at Camp Nou. It was the second injury blow for the hosts in the second half as Sergio Busquets was also replaced.
It went from bad to worse for Barcelona as Atletico levelled the scores in the 61st minute when Correa, who had only just come on, took advantage of a mistake from Gerard Pique before finding the bottom corner with a fine finish.
Atletico seemed intent on going for Barcelona in the minutes after the equaliser, but it was the home side that were dominating in the latter stages and Neymar brought a save from Oblak after skinning Juanfran 10 minutes from time.
Pique was next to come close for the home side after meeting a late free kick from Neymar, but the centre-back's header dropped wide of the post, before Jordi Alba fired over late on. Atletico actually had a chance to nick it in the 89th minute, only for Ter Stegen to keep out a bullet Diego Godin header.
Next up for Barcelona is a trip to Sporting Gijon on Saturday, while Atletico will attempt to return to winning ways when they host Deportivo La Coruna on Sunday afternoon.