.Steelers, who had been beaten in six out of their last ten matches, including their last three, were 0-2 down in the first six minutes, as their defensive coverage again gave coach Tom Barrasso cause for concern.
And despite dominating much of the rest of the game, they lost their fourth consecutive outing - Sheffield are still looking for a victory in 2019.
Stars' coach Omar Pacha had lost all previous 29 games he'd coached against Steelers for Hull, Manchester and Dundee.
But Pacha richly deserved his win at the 20th attempt.
It is the first time in the modern era that Dundee had won in Sheffield.
Earlier, with Mark Matheson in the penalty box for hooking a breakaway opponent, Fabrizio Ricci scored on the power play.
And when Josh McFadden slipped to the ice on the left flank, space opened up for Drydn Dow to score a memorable individual effort.
Third from bottom Stars' transition was a worry - and their forecheck was impressive on Arena ice.
And Steelers were fortunate Brandon Whistle's careless cross-ice pass wasn't punished more by Lukas Lundvald.
Sheffield's offence looked promising when John Armstrong got going with his long stride.
And they pulled one back when Jonas Westerling - who seconds earlier had been hit on the foot by a Ben O'Connor shot - set up Mark Matheson to score.
But Stars restored their two-goal advantage when Ricci struck home his second of the night.
Sheffield sustained 20 minutes of almost complete pressure in the middle period, although they lost Evan McGrath for a while with a facial injury.
And Dowd's giveaway afforded a chance to Francois Bouchard, whose shot was glove-saved by Jackson Whistle.
Finally, Steelers got a reward for their non-stop attacking, Dowd making up for his error with a shot from between the circles, on the power play.
McGrath had a mixed start to the last session.
He limped off with another injury but returned to play a part in the 3-3 equaliser, hammered in by Ryan Martinelli at 47:14.
Then a jumble of penalties was costly for the home sided.
McGrath was felled by Matt Bissonnette to go on the power play.
But first Dowd and then Aaron Johnson were dispatched to the sin bin and ex Steeler Matt Marquardt scored a fourth.
Then a long shot caused panic around Whistle's net and Francois Bouchard nicked in a fifth, the Scots' third power play success of the evening.
Whistle was pulled from goal for the extra skater with two minutes remaining - and paid the cost with an empty net goal from hat-trick man Ricci