Cape Verde had Carlos da Graca sent off on 55 minutes after he conceded a penalty, which was duly slotted home by Morocco striker Youssef El Arabi.
Six minutes later El Arabi struck again to double his side's advantage.
Morocco go through as group winners, leading Cape Verde by six points and having already beaten them twice.
There are two rounds of Group F matches remaining but while Cape Verde could potentially draw level on points with the Atlas Lions they would finish below them because of their inferior head-to-head record.
Cape Verde must aim to collect maximum points from their games against Sao Tome and Principe and Libya and hope to make it to next year's finals in Gabon as one of the two best group runners-up.
Morocco's passage to next year's tournament means their recently appointed coach Herve Renard will have the chance to win a third Nations Cup title - with a third team.
The Frenchman is looking to achieve back-to-back titles, following his success with Ivory Coast last time out. He also won with Zambia in 2012.
Morocco became the first team to qualify for the 2017 Africa Cup of Nations after beating Cape Verde 2-0 in their Group F match on Tuesday.