Sweden was already ready for promotion before the final match, but now won the group before the home nation Portugal who also goes on.
Both teams won three of four matches, but Sweden placed ahead thanks to a better goal difference in the mutual matches.
Luxembourg lost all four of their matches and are eliminated.
Sweden crushed Luxembourg earlier in the qualifiers with 53 points, but rested in this match for example the key player Ludde Håkansson.
Sweden started shakily and was down 16-19 at the end of the first period, but then scored 14 straight points and pulled away.
Charles Barton was the best scorer with 22 points and Alexander Lindqvist scored 21.
The next phase of the World Cup qualifiers starts in November.