Sweden, the reigning Olympic champions who are skipped by Anna Hasselborg, went ahead in the second end when the skip hit out a Danish stone to score three points.
A further two points in the fifth end helped secure a 6-3 victory over Denmark as the team impressed in front of their home crowd.
"That was a really good first game of the championship," Hasselborg said. "It was fun to get started. This is our first championship in Sweden, and we have been looking forward to this a lot."
World champions Switzerland faced European bronze medallists Germany in a hotly contested first round robin match.
Switzerland had a 3-1 lead at the conclusion of the third end, but Germany responded to tie the scores 3-3 in the fourth end.
In a tight encounter Germany edged ahead in the ninth end but Switzerland scored two points in the tenth to seal a 6-5 victory.
Scotland came out on top against Norway in their opening encounter, in a tight contest Norway had a slim 2-1 lead at the end of the third end.
In the fifth end, Scotland skip Eve Muirhead tapped out a Norwegian stone to reduce Norway's lead to 3-2 and the Scots scored points in the last four ends to triumph 7-4.
Elsewhere Russia cruised to victory against Estonia, who won promotion from the B-Division last year, defeating them 7-1 while Czech Republic comfortably defeated Latvia 8-2.