The result at the Wanda Metropolitano was enough to keep Real top of the early-season La Liga table, with the team unbeaten as they look to wrest the title back from champions Barcelona.
This was the third time in the last three seasons that the two great city rivals have ground out a goalless draw, having managed only six goalless games between them in their history previously.
It was also the second time the pair have drawn without scoring at Atletico’s new stadium, matching the number of blanks they managed at the old Vincent Calderon Stadium.
Real sit top of the league despite only winning four of their seven games so far this season.
Last weekend’s 2-0 win against Osasuna built on the 1-0 win they earned against Sevilla on the previous matchday meaning they are now enjoying a record-breaking run under Zidane.
Against Atletico, Karim Benzema nearly snatched the victory for Real with his headed effort 15 minutes from time at the Wanda Metropolitano, forcing a great save out of Jan Oblak.
Joao Felix and Saul Niguez went closest for Atletico, who registered just one attempt on target as their winless run in competitive meetings with Madrid stretched to a seventh match.
Atletico put seven goals past Madrid in July's pre-season clash in New Jersey and looked the more likely side to make a breakthrough in the first half of this latest showdown.
Joao Felix twice went close for the hosts, dragging a shot wide of the target with the angle against him and blasting narrowly wide from 25 yards.
Champions Barcelona made it back-to-back league wins with a 2-0 win over Getafe earlier on Saturday, offering hope they have turned a corner following their slow start.
It is Real who are out in front at the top of La Liga, though - this draw moving them one point clear of Atleti and surprise package Granada, while Barca are a further point behind.