A late goal means Dundee can play their favoured counter-attack game at home tonight and have an advantage in qualifying for the Nottingham finals.
Sheffield have now been shut out twice in three games.
They matched Dundee's effort and will. But that's all they did, not able to find the moment of quality around the opposition's crease.
Coach Aaron Fox said his team competed hard, in true play off manner, but were caught by the "best line rush team in the league" who know how to play the transition game.
The first period was about brute force and energy, proper play off stuff.
Dundee had the cleanest chances, Alexandre Ranger hit the post after three minutes Drydn Dow fired over the cross bar and home goalie Barry Brust, making only his second start in 16 games, foiled Ranger with a save which justified his choice in goal.
Keeton Ellerby performed wonders when he was left the last man standing on a two-on-one Stars' raid.
Sam Jones, rattled by Dundee's aggressive attitude, dropped the gloves and launched himself at Kyle Haas.
Martin Latal and Adrian Saxrud-Danielsen put goalie Adam Morrison under pressure before the first break, but a tied session was what both sides merited.
Steelers' best chance of breaking the deadlock in an even middle period came via Latal's piercing runs from either flank - four times he gave Morrison work to do.
But Brust still had to pull out a top drawer save when the Stars' top scorer Charlie Combs threatened.
The final session was 20 minutes of chopping, whacking, hustling and shot blocking.
John Armstrong drove in from the right wing to create a chance for Sheffield and Brust denied Michael Poirier.
But Dundee scored the goal their noisy supporters craved when Sebastian Bengtsson was alone at the back door to plant the puck home after Timi Lahtinen had done all the hard work down Sheffield's left flank.
Fox said the weekend series was a 120-minute hockey game - and they would have to find a way to score this evening.