And Griezmann levelled for third-placed Atletico when he slid home Angel Correa's through ball in the 85th minute.
"That is the way the score remained until two minutes from time, when Sevilla, who had honoured departing sporting director Monchi" before the match, finally finished off Depor with top scorer Wissam Ben Yedder netting his 10th league goal of the season.
Barcelona will go top on goal difference if they win at Malaga later on Saturday, although Real will have a game in hand.
"You couldn't say that Atletico put in a great performance, we certainly did, but we had to get that second goal, which would have given us that peace of mind".
With the likes of Cristiano Ronaldo, Karim Benzema and Gareth Bale as their front three, the home side are certainly the favourites to take the three points in this one and can be backed at around 8/11.
The France global netted his 15th LaLiga goal of the season with five minutes of normal time left to play to cancel out Pepe's earlier header and salvage a 1-1 draw for Atletico Madrid.
"We know we are a strong team, with a great mentality".
Atletico, though, remained unsafe on the counter-attack, as Griezmann made the most of a loose pass from Sergio Ramos and sent a low shot goalwards which Navas pushed behind at full stretch.
Liverpool have made the first move in the pursuit of Atletico Madrid owned left-back Theo Hernandez, reports Spanish publication Cadena SER.
Nothing went right for Barcelona.
It means that captain Sergio Ramos is likely to be partnered by Nacho when Madrid face Bayern Munich in the first leg of the Champions League quarter-final next week.
Unlike his counterpart in the Real Madrid dugout, Diego Simeone has quite a few injury concerns to deal with, with as many as six players sidelined due to fitness issues for the cross city trip to the Santiago Bernabeu.