Paul Thompson's side bounced back from Challenge Cup difficulties to take a League match lead over Dundee Stars inside five minutes.
Levi Nelson did the damage and five minutes later Jeff Legue added a second.
Sheffield were coasting and Jace Coyle, such a danger when he roams forward from defensive duties, made it 3-0 at 16;14.
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The second period was another shot-fest, with Mathieu Roy scoring at 26;07.
Two minutes later power forward Guillaume Desbiens got on the score sheet to gain some reward for his hard work on the wing.
On-form centreman Tyler Mosienko made it 6-0 at 34;12.
After that, all that was required was an efficient closure, with a Sunday night trip to Coventry in mind.
But Conny Stromberg rubbed it in with a late last seventh goal.
*Elite League leaders Cardiff continued their wobble on Saturday night.
The Devils were beaten 2-1 on home ice by struggling Coventry Blaze - the Welsh side's third successive defeat.
Belfast Giants moved to within five points of the top two with a fifth straight win - 2-1 over a Braehead Clan side beaten for the fifth successive game.
Saturday 27th February
Braehead Clan 2 Belfast Giants 5
Cardiff Devils 1 Coventry Blaze 2
Sheffield Steelers 7 Dundee Stars 0
Sunday 28th February
Braehead Clan v Nottingham Panthers – 6.00pm
Coventry Blaze v Sheffield Steelers – 5.15pm
Dundee Stars v Manchester Storm – 6.30pm
Edinburgh Capitals v Fife Flyers – 5.30pm