Atleti remains top, two points clear of nearest rival Barca, but Los Blancos will take over if they beat fourth-placed Sevilla on Monday (AEST) courtesy of a better head-to-head record against Diego Simeone's side.
Despite dominating the first half, Atleti could not find a way past Marc-Andre ter Stegen, the German making six saves before the interval.
Barca improved after the break, but Ronald Koeman's team ultimately fell short of finding a winner that would have moved it to the summit.
Atleti, which saw Thomas Lemar forced off with an injury early on, almost went ahead shortly before the midway point of the first half, Angel Correa denied what looked set to be a certain goal by a superb last-ditch block by Clement Lenglet.
Barca lost Sergio Busquets in the 32nd minute after a clash of heads with Stefan Savic, before Ter Stegen kept out Marcos Llorente, Luis Suarez and Yannick Carrasco in quick succession.
Lionel Messi was denied a memorable goal shortly before the interval, Jan Oblak wonderfully tipping the Argentina international's effort away after he had waltzed past a host of Atleti players.
Simeone's visitors should have made their first-half dominance count on the stroke of half-time, yet Felipe blazed over from 10 yards after being picked out by Llorente.
The hosts did most of the pressing at the start of the second period, Oblak forced to paw away a Messi free-kick after 66 minutes.
Ronald Araujo had a header ruled out for offside soon after, while fellow substitute Ousmane Dembele nodded over from a glorious position five minutes from full-time as Barca threatened to claim all three points.
Atleti did not look like snatching a goal in the closing stages as its winless run at Camp Nou was extended to 15 games.