The champions dipped 2-1 at Belfast, although they were level in regulation time, before losing in overtime.
Belfast outshot Sheffield 32-27 - and the victory severely affects Steelers championship defence.
But at least Paul Thompson’s men got a point.
First line winger Colton Fretter opened the scoring, via assists from John Armstrong and Mathieu Roy in the third period.
But ex Steeler Colin Shields hit back just 22 seconds later, assisted by James Desmarais and Steve Saviano.
It was incredibly tight.
But Giants grabbed the win through top scorer Chris Higgins (assts Blair Riley, Derrick Walser) just 31 seconds into the extra session - although the play appeared to be off side.
The win for Giants took them seven points clear of Sheffield.
The teams play again tomorrow night at the same venue.
Saturday 7th January
Belfast Giants 2 Sheffield Steelers 1 (OT)
Cardiff Devils 3 Coventry Blaze 4 (OT)
Edinburgh Capitals 3 Dundee Stars 2
Manchester Storm 2 Fife Flyers 4
Nottingham Panthers 4 Braehead Clan 3 (OT)
Sunday 8th January
Belfast Giants v Sheffield Steelers – 4.00pm
Braehead Clan v Cardiff Devils – 6.00pm
Coventry Blaze v Nottingham Panthers – 5.15pm
Dundee Stars v Edinburgh Capitals – 6.30pm
Fife Flyers v Manchester Storm – 6.30pm