The away side controlled the first period in the Spanish capital, with Costa's cool finish enough to leave them ahead at the interval.
Both sides had opportunities in an entertaining second period, but Atletico closed the match out to secure a vital three points and continue their 100% start to the season in the process.
Here, Sports Mole dissects the 90 minutes of action between the two capital rivals.
On target: 5
On target: 4
Was the result fair?
In a word, yes. It was no fluke when Atletico took the lead in the 11th minute and but for some poor finishing, they could have had daylight at the interval. It was a similar story in the second period and although Real Madrid had their chances, it would have been a travesty if Atletico hadn't picked up all the points. Diego Simeone has taken his side to Barcelona - albeit in the Spanish Super Cup - and now the Bernabeu this season, and been the better team on each occasion. It is back to the drawing board for Real Madrid, however, who had no answer to their rivals this evening.
Real Madrid's performance
When Real Madrid fell behind, a response was expected. They did increase the tempo in the latter stages of the first period, but without really threatening to open their tally for the evening. Gareth Bale and Luka Modric were introduced at the interval, but neither really had much of an influence on proceedings. They might have an incredible wealth of attacking talent, but there remains serious questions about their defence with the partnership of Pepe and Sergio Ramos not exactly filling the supporters full of confidence. Granted, it is early in the season, but they are already five points off the early pace, which is being set by both Barcelona and Atletico.
Atletico Madrid's performance
In terms of away performances at the top level, it was just about as good as it gets for Atletico. There isn't a team in Spain that works harder than the capital outfit, while with the likes of Arda Turan, Koke and Gabi, they have the technicians to compliment their incredible work-rate. It was not a fluke performance from Atletico, who have been simply sensational throughout the early stages of the season. This result and indeed performance indicates that they can challenge for the league title this season.
Sports Mole's man of the match
Diego Costa: Love him or loathe him, you just cannot ignore Costa. He won his personal battle with Ramos this evening, while he ran the entire Madrid defence all over the pitch until he was withdrawn in the latter stages. Of course, he was booked, but it was just about the perfect centre-forward performance from the Brazilian, whose goal has moved him onto eight league strikes for the season. Arguably, in this type of form, he is the best number nine in the world.
Biggest gaffe of the match
Only Angel di Maria will know what he had in mind in the build-up to Atletico's goal. Instead of playing a simple pass to his left, he decided to dribble between two players - Koke picked the Argentine's pocket, before feeding Costa, who expertly finished into the bottom corner. Di Maria was hooked at the interval, which came as no great surprise.
Antonio Mateu must be praised for his performance in the Spanish capital this evening. As expected, it was a feisty affair with a number of off-the-ball incidents throughout the 90 minutes. However, the Spaniard was sensitive to the occasion and although he produced eight yellow cards - four for each side - he refused to issue a red card, despite a couple of players coming close to leaving the field. Overall, neither manager will have had many complaints about his performance at the Bernabeu.
Real Madrid: Carlo Ancelotti's side are in Champions League action at home to Copenhagen on Wednesday, before they travel to Levante in the league next Saturday.
Atletico Madrid: Atletico are also in Champions League action next week as they travel to Porto, before welcoming Celta Vigo in La Liga next Sunday.