Barca were heading for their first defeat of the season after a Saul wonder goal in the first half but eight minutes from time Suarez struck with a far post header from Sergio Roberto’s deep cross.
Barcelona were dealt the body blow of losing Neymar in the summer and when the spent a fortune on his replacement Ousmane Dembele he picked a three-month injury.
For now at least Suarez and Lionel Messi are more than keeping Barcelona afloat, they are keeping them clear of the field in La Liga.
Barcelona took the game to Atletico in the early minutes with Messi almost breaking through a packed penalty area only for the ball to be cleared for a corner.
In the four man midfield behind them Andres Iniesta had Barcelona’s first chance which Jan Oblak pushed away.
Busquets bamboozled Saul with flick and a turn that sent him one way and the ball the other but Atletico Madrid were finding their stride and Marc Andre ter Stegen save brilliantly when Antoine Griezmann shot to his near post.
Griezmann had started well and in one of countless raids forward he pushed the ball through Gerard Pique’s leg inside the area only for Ter Stegen to save his shot.
If this was Griezmann’s trial for a move to Barcelona next season he was passing with flying colours.
It was another player who Atletico will pray stays put in the summer who got the opening goal, however and once Saul’s cracker from the edge of the area had flown in Atletico were very much in their favoured territory.
They sat deep and allowed Barcelona to come on to them and there was no way through the massed red-and-white striped ranks.
That pattern remained in the second half and Barcelona were not helping themselves with their final ball.
Suarez found Jordi Alba with a perfect ball over the top but the full-back’s cross was awful and went beyond everyone. Suarez then had a shot saved by Oblak and Messi went close with a free-kick.
Valverde made a double change bringing on Gerard Deulofeu and Sergi Roberto for Andres Iniesta and Nelson Semedo but the masterplan still seemed to be feed Messi and let him find away through.
His shot was well turned away by Oblak. He took aim again from the edge of the area but this time sent the ball the wrong side of the far post. Could it really be that he used up all his magic for one week on international duty?
It didn’t matter in the end because Suarez had held some back. He got the late equaliser and still no one has beaten Barcelona in the league this season.