Gemma Grainger's side have won both of their games in Switzerland so far and, with head-to-head operating as the tiebreaker, they cannot now be caught by either the hosts or Finland.
Norway took the lead when Eva Nystrom diverted a cross into her own net in the third minute.
But Finland grew into the game and deservedly equalised through Oona Sevenius.
Lisa Naalsund was brought on in place of Vilde Boe Risa at the break, as Norway attempted to find a winner.
It was Caroline Graham Hansen who struck with six minutes to go, her attempted cross finding the net via the back post.