The Olympic bronze medalists from Beijing had taken over the match throughout, but after the eighth round, the Danish skipper Madeleine Dupont and her teammates almost caught up, with 5-4.
Sweden then made sure to answer with a four-pointer in the ninth round.
The Danes gave up and Sweden's victory numbers were written 9-4.
This means that Sweden has started the curling WC in Prince George in Canada with two victories and one loss.
Earlier in the day, the Swedes lost 7-8 to Switzerland.
The World Cup began for team Hasselborg the night before Sunday with a victory against Turkey with 9-6.