Just four years after being admitted to a competition from which they had been excluded for several years, this first trophy success - it was clinched when they beat the holders, Braehead Clan, 3-1 at Dundee Ice Arena - is a landmark achievement.
Becoming the first Scottish side to reach the play-off finals in the only major professional team sport to boast a genuine pan-British league, would be even more significant because, true to the North American associations of the sport, the knockout finale is considered more important than season-long standings.
While the Stars' task is now to maintain momentum ahead of what is effectively a home and away quarter-final round that acts as an eliminator for the play-offs, an extra element of intrigue is also added by the prospect of guaranteed Scottish involvement should they meet Fife Flyers in the last eight.
"To have a local derby at that stage would be ideal, but the big thing for us is to get to Nottingham," said Steve Ward, the commercial director who owns the club along with his brothers Mike - the former Dundee Rockets netminder who is now the Stars' director of ice hockey - and Charlie.
The slightly convoluted system means that the dominant Belfast Giants - they are runaway winners of both the Erhardt Conference and the overall Elite League, are top seeds so will meet the eighth-ranked side in the eliminators. Dundee's Gardiner Conference triumph makes them second seeds, so they meet the team that finishes seventh.
Third to eighth places are decided on the overall Elite League positions rather than Conference placings, with third facing sixth and fourth meeting fifth. Sheffield Steelers look pretty secure for third place, Nottingham Panthers are favourites for fourth and Braehead Clan fifth, while Coventry Blaze, Hull Stingrays, Cardiff Devils and Fife Flyers are all in contention for the remaining three berths.
As Scotland matches England in supplying 40% of the participating teams, it is remarkable that the play-off breakthrough has yet to be made. That, though, is partly down to the historic issues that led to Dundee, along with Fife, being marginalised when the old British National League folded in 2005, leaving them playing at a lower standard in the Scottish National League, in which their feeder team, Dundee Comets, now feature.
Along with Belfast and Cardiff, Edinburgh were, as the team from the capital city, asked to provide the sole Scottish representation in a then English-dominated Elite League, but Dundee, along with the newly- formed Braehead Clan, were invited to join in 2010, with Fife following a year later.
Together, the four sides are, as a Scottish professional club sport, second only to football in terms of spectator interest. Each club play some 60 matches in all so average a home match every week at which the combined attendances at the indoor venues are around 7000. With rosters built around gnarled imports who encourage professional attitudes as well as introducing locally developed talent to the finer points of the sport, that North American-influenced mix of hardcore competition and entertainment is compelling.
Ward believes aspirations should be higher still, though. "The goal for British ice hockey has to be to get a team to the Olympics," he said, while acknowledging that a sport with a history of political infighting has work to do to bring its various governing bodies together towards that purpose.
Meantime, his focus is wholly on Stars and trying to build on a win that brought a nervous wait to an end. "We've done it with four games to go but it was a relief to clinch the Conference at the first time of asking because we had three chances to win it last season and didn't," Ward said.
"We had three matches on the final weekend, against Edinburgh twice and Braehead, needing to win just one of them and lost the lot. When I knew the trophy and medals were here, I didn't touch them until we had beaten Clan this time. Our goal for the season, though, was to win the Conference and to reach the play-offs. We're halfway there."