A late revival ended in an overtime winner from Nikolay Lemtyugov, to keep Sheffield's EIHL rivals at bay.
With Cardiff Devils having four games in hand, things were looking bleak until the Yorkshire side showed resilience in the dying moments.
Steelers had gone into the game after Saturday's not-altogether-convincing 4-2 victory over Manchester Storm.
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Their supporters had only to wait 21 seconds for the first goal, Marco Vallerand crashing in.
Sheffield sought to maintain game ownership with some meaty checks from Tanner Eberle and Davey Phillips.
But Blaze are an improving side. They'd won their last three matches and had scored more than any other EIHL team, except Sheffield.
It was no surprise when they netted twice. First, American defenceman Dillon Eichstadt chipped in at 6:57.
Then, their most lethal sniper Luke Ferrara put them ahead at 8:02.
Sheffield goalie Tomas Duba recovered his composure by denying a big Andrew Johnston shot
And in the opposite crease, Blaze's new custodian C.J. Motte pulled off a tremendous save from Eberle.
The goalie's tripping of Eberle led to a power play though and the Sheffield No 10 made it 2-2 at 29:20.
Coventry hit back, exposing a lack of marking at the back post, allowing Johnston to chalk up Blaze's third.
And with Aaron Brocklehurst sitting out Steelers' first penalty of the night, they had to work hard to go in at the second break just one goal down.
Some of the 2,474 home fans may have detected tiredness in the Steeler ranks.
Yet there was no sign of that when Vallerand got his third point of the night, helping Eberle tap into the net for his second goal, at 43:29.
Still, Steelers could not shore up at the back and Evan Bloodoff's wrister gave Coventry the lead for the third time.
They conceded to a one-timer from the same player 99 seconds later on the power play.
But Sheffield dug deep: a power play effort from Marek Troncinsky reduced the deficit before Lucas Sandstrom joyfully made it 5-5 with 76 seconds left.
The stage was sent for their Russian winger to bring home both points.