Matt Beca scored the crucial penalty shot to take victory for Glasgow Clan, but their Challenge Cup fate remains in the balance.
Only when all the groups are concluded next month will it become clear who will qualify for the last eight, but Pete Russell’s men had to dig deep.
Clan got the perfect start when Travis Ehrhardt tapped in from close range after Brendan Connolly fed Matt Beca in the centre, who tapped it on for the finish.
A blue line effort from Matt Stanisz went close as Dundee goalie Pontus Sjögren had to make the crucial stop to keep the difference at one goal.
Scott Tanski saw a good chance denied after being sprung from the penalty box straight into a breakaway, but he fired over.
Clan were tested at the other end when netminder Joel Rumpel managed to get his pad on a powerful Matt Marquardt drive, sending it into the nets behind.
The home side doubled their lead early in the second when Jack Musil struck one from the left, sending the puck into the top corner for his first ever Clan goal.
Then Craig Peaock swept in a third at the back post after a pass from Rasmus Bjerrum found its way to him across the crease.
Stars began to hit back and gained some timely momentum with two goals in the final minute of the second period.
Matt Marquardt got the final touch after Lukas Lundvald had struck the post to get Stars on the scoresheet.
This was quickly followed by a François Bouchard shot that was turned in by Mike Sullivan as Clan’s three-goal lead was whittled down to one.
It didn’t stop there when Bouchard pulled the Stars level early in the third, then the visitors went in front through Matt Marquardt as the night started to take a worrying turn.
Glasgow managed to pull level with eight minutes to go when Tyson Wilson showed great tenacity to hold on to possession of the puck to allow Gerard Hanson to tap home.
The game was tied and went the distance, going all the way to penalty shots where Bjerrum and Beca were successful, the latter’s confirming the victory.