The Danes took bronze in last year's WC and have been favorites beforehand, along with Sweden, to take home the group.
But Slovenia seems to want to set the hook for the big Nordic teams.
Denmark had big problems with the Slovenian defense and failed to increase the pace of the match.
With just over five minutes remaining, the home team had gained momentum and went away to a three-goal lead.
Big star Ana Gros managed eight goals despite spending much of the second half on the bench in what ended up being a two-goal victory for Slovenia.
Sweden face Slovenia in their second match of the championship, on Sunday, and finish against Denmark on Tuesday.
The three best teams advance to the main round, where they take with them the points they scored against the other advancing teams in the group stage.