The win at Ice Sheffield leaves Paul Thompson’s team 10 points adrift of leaders Cardiff Devils ahead of their visit to South Wales on Saturday night.
Two goals in three first period minutes put Steelers on the road to victory against a Stars side who came into the fixture on the back of a three-game losing streak.
Mike Ratchuk got the first marker on the board after he won possession of the loose puck and sent a shot past Stars goalie Joe Fallon at 14.11.
Steelers only had to wait a couple more minutes when defenceman Jace Coyle, making his first appearance since returning to the club less than 24 hours earlier, dived at the crease to turn it into the net.
Dundee halved the deficit midway through the second when Felix-Antoine Poulin found the net, only for John Armstrong to restore the hosts’ two-goal lead at 33.54.
Luke Ferrara added a fourth when he finished off a good passing move at 48.11 and although Brett Switzer was on target for Dundee’s second, the Steelers kept hold of their lead to take the points.