Barcelona cruised to a 3-0 win over Leganes earlier on Saturday and the subsequent derby stalemate means the Madrid sides are now 10 points behind Ernesto Valverde's high-flying Catalans.
Diego Simeone and Zinedine Zidane's sides have both fallen short of expectations so far this campaign and failure to win such a high-profile game will increase the strain on the two head coaches.
The best opportunity of the game came in just the third minute when Angel Correa clipped wide from an excellent opening after inadvertently being played in by Real Madrid defender Raphael Varane.
Karim Benzema and Cristiano Ronaldo struggled to make any significant inroads against Atletico's obdurate defence, which means the star forwards have now scored just two goals between them in a combined 16 league appearances this season.
Atletico and Real Madrid know they must register wins against Levante and Malaga respectively next weekend if they are to get their stuttering league seasons back on track and stand any chance of closing the significant gap to Barca.
Atletico started at a blistering pace and should have been ahead inside three minutes courtesy of some kamikaze defending by Zidane's men.
A poor pass from Marcelo put his defence under pressure and after numerous failed attempts to clear the ball it eventually fell invitingly to Correa, but the Argentina international contrived to steer his shot over the onrushing Kiko Casilla and agonisingly past the left-hand post.
Gabi fired a speculative long-range volley off target midway through the first half before the visitors hit their stride and carved out a number of clear opportunities to take the lead.
After some clever passing on the edge of the Atletico penalty area, Cristiano Ronaldo released Toni Kroos but the Germany midfielder could only scuff his shot into Jan Oblak's side netting.
This was followed soon after by a dipping Ronaldo free-kick from 35 yards that Oblak turned around the post and a close-range header from Sergio Ramos that flew wide.
Ramos took a boot to the face from Lucas Hernandez in that incident, suffering a suspected broken nose, and was withdrawn at half time in place of Nacho.
The second period failed to bring about a change in fortunes for either side, with both defences standing firm and repelling almost every attack.
Benzema's disappointing evening came to an end in the 76th minute as Zidane threw on Marco Asensio in a bid to inspire a late winner.
It was the hosts that came closest to breaking the deadlock and securing a famous win, though. Substitute Kevin Gameiro lifted a shot over Casilla, but the backtracking Varane brilliantly headed off the line to deny what would have been a certain winner that, in truth, neither side deserved.
Key Opta Stats:
- Real Madrid have failed to score in a LaLiga away game for the first time under Zinedine Zidane (35 games).
- This was the first 0-0 between the two teams in LaLiga since May 2005 at Santiago Bernabeu and the first with Atletico at home since October 1993.
- Atletico have equalled their best start without a defeat in La Liga history (W6 D6), recorded in their famous season of 1995-96 when they went on to win the double of league and Copa del Rey.
- Atletico have also set their longest unbeaten run in LaLiga under Diego Simeone (16 games, W9 D7).
- Antoine Griezmann is currently on his longest goalscoring drought for Atletico in all competitions (eight games in a row - 723 minutes).