Having lost Friday's opening tournament game 5-1 to Nomad Astana, Sheffield were two down in 10 minutes to the hosts and favourites, Yunost.
Klemen Pretnar tipped the Belarus side ahead on home ice at 3;28 on the Power Play .
Then Andrei Antonov doubled the lead and must have thought they were strolling to a fourth Continental Cup success.
But injury-plagued Sheffield showed defiance when they replied on 13 minutes, on the Power Play, when Mathieu Roy scored from Colton Fretter and Andreas Jamtin.
And Roy shocked the Belarussian hosts with his second of the night just before the first interval, scoring from Scott Aarssen at 18;18
The display rivals any first period Sheffield have played at home or abroad this season.
And it showed the side has got guts and character.
Steelers thought Roy had got his hat-trick at the start of the second session, but a video study ruled the puck had not crossed the line.
That back luck cost them.
Steelers went behind when Alexander Kogalev nipped ahead of Aarssen to beat Ervins Mustukovs at 23;07 - but Mark Matheson wiped out that advantage with a fine equaliser at 24;37.
The British side then killed a five-on-three penalty, with Johnathan Phillips and Jonas Westerling outstanding.
But another penalty to Steelers, Davey Phillips serving a contested tripping minor, saw the Belarussians score their fourth, Alexei Yefimenko hitting the net at 43:07.
Astonishingly, Sheffield still had enough left in the tank to equalise again - d-man Matheson scoring his second at 52;13.
Considering they were without Miika Franssila, John Armstrong, Liam Kirk and Rob Dowd, it was an amazing achievement to fight back for a third time.
But with two minutes 27 seconds left, Sheffield were seemingly put to the sword, Andri Mikhnov scoring a decisive fifth.
Sheffield withdrew their goalie for six skaters, and Andreas Jamtin came within a whisker of equalising.
After the game, Ben O'Connor said he and others were "heartbroken" - but said they were proud of their performance tonight.
Coach Paul Thompson said considering he'd had just five defence at his disposal his team had "matched them all the way.
"Everybody was outstanding, if they had played on Friday maybe we'd be in a different position.
"The chemistry was very, very pleasing."