With the title wrapped up, Real made seven changes following their dramatic win over Manchester City on Wednesday.
Atletico started strongly and Yannick Carrasco converted what proved to be the winner from the penalty spot after Matheus Cunha was brought down.
Diego Simeone's side remain fourth, six points clear of Real Betis in fifth.
The Atletico boss roused the crowd with his arms as last season's title winners held on to a win that puts them just one point behind third-placed Sevilla.
The hosts missed chances to double their lead, with Angel Correa firing wide early on and Cunha seeing his shot saved after great work by Antoine Griezmann.
Griezmann and Carrasco also combined superbly in the box but the France forward fired wide of Andriy Lunin's goal, before Carrasco struck the inside of the near post moments later.
Real Madrid improved when Vinicius Junior was introduced in the second half and the Brazil forward's driving run set up a good opportunity for Marco Asensio, which was blocked.
Substitute Federico Valverde twice tested Atletico goalkeeper Jan Oblak in the end-to-end encounter at the Wanda Metropolitano.
Carlo Ancelotti's champions have three more league games to play before meeting Liverpool in the Champions League final on 28 May in Paris.
