Nottingham Panthers - a side re-building with three wins in their last four outings - were worthy opponents and twice took the lead in a seesaw encounter.
But the late winner by defenceman Mark Matheson saw Paul Thompson's on form men take maximum points, allowing them to reclaim fourth spot.
League leaders Cardiff Devils, though, beat second place Belfast Giants 2 Cardiff Devils and are major favourites to defend their title.
At Sheffield Arena, the visitors had scored as early as 1;52 - Raphael Bussieres outfoxing Miika Franssila in the corner and working the puck towards goal, where Ollie Betteridge scored.
Liam Kirk, watched this week by a Buffalo Sabres' scout, did his chances of being an NHL draft contender no harm by equalising 24 seconds later.
He skated unmarked down the left and was given plenty of time to rifle past a static Mike Garnett.
Matt Marquardt, playing his 100th EIHL game, threatened down the right wing on the first line unit.
But Sheffield conceded again, at 16;50, when Jeff Brown scored unassisted.
Panthers saw a lot of the puck at the start of the second and they increased their lead to 3-1 from Zack Phillips.
But Marquardt skated hard to the crease from the right flank and reduced the arrears at 28:37, Mark Matheson assisting.
It was the power winger's sixth goal in five games.
And it was 3-3 when Jonas Westerling scored on a five on three Power Play.
After such a difficult start of the match it was a breathless moment for the big Arena crowd to see Andreas Valdix give Sheffield their first lead of the net at 34:58.
That spelled to end of Garnett in goal, he was replaced by Patrick Galbraith
And the coach's statement seemed to work.
When Scott Aarssen took a two minutes interference call, 22-year-old Russian forward Mokshantsev fired in a power play equaliser from Robert Farmer and Yann Sauve at 53:37.
With five seconds left on the clock, Steelers preserved their immaculate home form with a back-handed winner from man of the match Matheson, who had skated rink-length to seize the points.
With 17 League games left, Steelers are in good form.
And with news of a new five-year contract with the Arena announced today, all is well.
Tomorrow, they meet Manchester Storm at the venue.
Saturday 3rd February
Belfast Giants 2 Cardiff Devils 3 (After Overtime)
Braehead Clan 3 Fife Flyers 2
Dundee Stars 5 Edinburgh Capitals 4
Manchester Storm 9 Coventry Blaze 1
Milton Keynes Lightning 2 Guildford Flames 5
Sheffield Steelers 5 Nottingham Panthers 4
Sunday 4th February
Coventry Blaze v Guildford Flames - 5.15pm
Edinburgh Capitals v Milton Keynes Lightning - 6.00pm
Fife Flyers v Braehead Clan - 6.30pm
Nottingham Panthers v Dundee Stars - 4.00pm
Sheffield Steelers v Manchester Storm - 5.00pm