The Spaniards were the brighter side in the first half but Juve went ahead in the 48th minute when Juan Cuadrado sent an unstoppable curling shot into the top corner after a break engineered by a punt forward from defender Leonardo Bonucci.
The Italian champions doubled their lead in the 65th minute following another quick counter as midfielder Blaise Matuidi headed home a cross from Alex Sandro.
But with bullish coach Diego Simeone motivating them from the sidelines and a typically boisterous Wanda Metropolitano crowd roaring them on, Atletico refused to give in.