Diego Costa’s 13th goal of the season helped Atletico Madrid return to within one point of leaders Barcelona and restore a five-point lead over Real with victory over Athletic Bilbao.
The striker’s clinical finish added to David Villa’s volleyed opener to secure an 11th La Liga win out of 12 matches.
And Costa has now moved level with Real’s Cristiano Ronaldo at the top of Spain’s top-flight goalscoring charts.
Bilbao were reduced to 10 men on 78 minutes when Erik Moran was sent off.
Valencia were the last team other than Barcelona or Real Madrid to win La Liga when they triumphed in 2004.
Only Villarreal have broken the stranglehold of the big two since, coming second behind Real and ahead of third-placed Barca in 2008.
Villa, who joined Atletico from Barcelona in the summer, opened the scoring in the 33rd minute with a well-taken volley to take his tally for the season to six goals.
And Costa, 25, doubled the home side’s lead seven minutes later when he raced on to a Koke throughball to fire past Bilbao goalkeeper Gorka Iraizoz.
Bilbao, who did not manage a single shot on target, played the final 10 minutes with 10 men after substitute Moran picked up two bookings. Following the defeat, Los Leones stay fifth on 20 points.
Defending champions Barcelona, 1-0 winners at home to Espanyol in Friday’s Catalan derby, have 34 points, with Atletico on 33 and Real, who beat Rayo Vallecano 3-2 on Saturday, on 28.