Aaron Fox's men were well worth this midweek win over Fife Flyers, and could have scored more.
It was another strong night for goalie Tomas Duba, playing his sixth consecutive game - and some of his side's offensive play in the first two periods was eye-catching.
Fife had started the night two points adrift of Sheffield with games in hand - and although they were mercilessly beaten 10-3 at home by Sheffield last Sautrday, they'd rallied on Sunday, with a 4-1 victory over Nottingham Panthers.
That big defeat is still smarting for them and their coach Todd Dutiaume had demanded a much tighter match.
And so it was in the first period, which started with Duba having to poke-check Tim Crowder to prevent the home side going behind.
In fact, Jonas Emmerdahl backed-handed wide, Mike Cazzola blasted over the bar and Danick Guathier floored Tanner Eberle with a giant hit as the Scots tried to prove a point to themselves and their hardy, travelling fans.
But Steelers had the clearer chances, and went ahead on four minutes, with a memorable Power Play goal.
Marc-Olivier Vallerand appeared to crash the puck against the pipework and Michael Davies reacted with blurring speed to the rebound, burying it beyond Adam Morrison.
Aaron Brocklehurst hit the side of the post on another PP - one of 18 chances on goal in the session.
Penalties defined the middle 20 minutes, with Flyers sitting out three minors in quick succession.
On the second of those, Robert Dowd wandered almost casually in from the left flank and made it 2-0.
Even when Sheffield's James Bettauer was called for tripping, it was the Arena team who profited, Tanner Eberle's splendid breakway no doubt bringing a smile to the faces of his parents, visiting from Canada.
But Dowd and Cole Shudra were both send to the penalty box at 33:01, giving the chance for Sam Jones to crash in a reply; 3-1, 21 seconds into the two-man advantage.
The Scots were back in the hunt and only the post stopped Carlo Finucci from adding a second.
And credit was due to them for the way they opened the game up, some desperate home defending, exhausting penalty-killing and fine goaltending from Duba was needed to stop James Livingston and Chase Schaber in the third.
It was a busy home debut for Mikko Kuukka on the blue line.
But the game was put beyond doubt by a Ben O'Connor empty-netter at 58:28.