Although the match failed to produce any goals, there was plenty of entertainment for the fans at Los Carmenes stadium to enjoy and both sides will feel they could have come away with the victory.
The result means that third-bottom Granada could celebrate their fifth point of the campaign since returning to the top flight, while Atletico move onto nine points after what they will feel was another disappointing result.
Atletico brought in a host of new faces this summer, including Radamel Falcao for a club-record 40million euros, as well as the likes of Arda Turan, Silvio and Diego, but tonight's draw means the Rojiblancos have just two wins from seven games so far and are already eight points behind the leaders in La Liga. They have also failed to score in five of those fixtures.
Gregorio Manzano's men had lost both their previous two away matches without scoring and that poor form looked like continuing tonight as Granada enjoyed a good start.
With just four minutes on the clock, Ikechukwu Uche looked to have given the home side the lead, but his header from near the penalty spot came back off the post with Atletico goalkeeper Thibaut Courtois well beaten.
Granada defender Inigo Lopez then headed a free-kick just wide before Dani Benitez missed a gilt-edged chance in the 20th minute when an Atletico defensive error left him one-on-one with Courtois, but his chip over the Atletico goalkeeper dropped just beyond the far post.
Soon after that Atletico had a great chance themselves, but Jose Antonio Reyes was denied by a superb one-handed save by Roberto Fernandez following a slick move by the visitors.
Granada were back on the attack in the 34th minute and Guilherme Siqueira saw his goal-bound shot blocked by a crucial last-ditch intervention by Filipe Luis.
Both sides continued to create chances after the break, with Diego firing over for the visitors and Courtois keeping out an Alexandre Geijo effort.
Roberto also did well to deny Atletico substitute Adrian Lopez as the away side started to turn up the pressure in the closing stages.
Adrian fired another opening over, and he then saw a late shot saved by Roberto as Granada held on for a point.