The result preserves Atletico’s 100 per cent start to the league campaign, putting them joint top on 21 points out of 21 with Barcelona and supporting their case as genuine title contenders this season.
Atletico started the better of the two teams, pressing Real Madrid hard on the ball, and indeed Diego Simeone’s team took the lead after 11 minutes through Costa. Koke took advantage of Angel Di Maria’s slack play on the edge of the to thread through Costa and the striker made no mistake, slotting past Diego Lopez.
And the visitors should have doubled their lead just minutes later when Tiago headed over unchallenged from six yards after being found by the impressive Koke from a corner kick.
Real Madrid struggled to get to grips with the contest and had Lopez to thank for keeping the score at 1-0 just before the break, with the Spanish keeper pulling off a reflex double save, first from Miranda before blocking at the feet of Costa.
Ancelotti introduced Bale and Luka Modric at half time in an attempt to turn the tide of the contest, but Real Madrid’s struggles in the final third continued in the second half.
Atletico’s pace on the counter attack was proving a problem for Pepe and Sergio Ramos and it provided Costa with another glorious chance to extend his side’s lead, but after breaking through one-on-one his touch was poor and Lopez smothered the eventual shot.
Modric’s presence in the centre of the field meant Real Madrid enjoyed a larger share of possession after the half, but with Isco enduring a difficult evening the attacking burden was placed on Cristiano Ronaldo and Bale.
However, once again it was Atletico who looked more likely to find the net for a second time, with Simeone’s team ruing their misfortune after Koke struck the bar with a curled effort from 12 yards.
The substitution of fans’ favourite Alvaro Morata was Ancelotti’s final throw of the dice with the clock winding down, but despite the youngster’s physical presence in attack Atletico held firm for a famous victory.