A hard-fought match between the two Spanish rivals saw chances few and far between, although Barcelona had the better of the match.
Atletico, who were without several key players due to positive Covid-19 tests, also had goalkeeper Hedvig Lindahl in fine form to deny Barca.
The Catalans finally made their dominance pay late in the game when Kheira Hamraoui scored the winner with a low shot into the corner on 80 minutes.
Barcelona thought they should have had a penalty afterwards when Alexia Putellas was brought down but nothing was given.
Yet Barca did enough for victory and progress to a semi-final against Wolfsburg on Tuesday in San Sebastian. The German side booked their place in the last four with a 9-1 win over Glasgow City.