Pete Russell's team would have started their opening day clash in Division 1A very much as second favourites but - despite being outshot by more than two-to-one - produced a memorable performance to seal a 3-1 victory.
It sets them up well for the rest of the week with their next game coming against another pre-tournament big-hitter in the form of Kazakhstan on Tuesday.
Sheffield Steelers' Ben O'Connor and Rob Dowd both got on the scoresheet for GB, with the third coming from the stick of Brett Perlini.
The much-fancied Slovenians - who recently played in the Pyeongchang Winter Olympics and were relegated from the top tier of the world game last year - piled on the pressure in the third period, unleashing 18 shots on the goal of Rotherham-born netminder Ben Bowns, but he stood tall to back-stop his team home to a memorable win.
"That was very special indeed," said head coach, Russell. "To beat a side who played in the Olympics this year is a fantastic achievement. The boys gave it everything and put it all on the line. I am very proud of them.
"We were outstanding all across the ice - they were real heroes out there. This a great start but we must not get ahead of ourselves and we still have four massive games to come."
After dealing with the anticipated early pressure, GB more than held their own and, with Ziga Pavlin in the box on a tripping call on Mark Richardson, the puck was eventually worked to O'Connor who rattled one past Gasper Kroselj into the roof of the net.
The Slovenians levelled at 12.22 with a well-worked move which left GB thinly-stretched and allowed Blaz Gregorc to slot home past a helpless Bowns.
The Cardiff netminder had to be at his best to keep out shots from Rok Ticar and Jan Urbas on the powerplay while, at the other end, Cardiff's Matthew Myers shot just wide of the right-hand post.
But GB ensured they took a lead into the second break when, at 35.59, Steelers' Dowd was quickest to react to a spiralling puck which flew back and up into the air off the plexiglass behind the net to where he was stood waiting just front of netminder Kroselj, who reacted too late.
Just under five minutes into the third, it got even better for Russell's team when a well-worked move saw O'Connor feed Mike Hammond, who in turn found Perlini free to sweep the puck home at the back post.
Not surprisingly, there were moments of desperate defence from GB in the closing minutes as the top seeds strived to get themselves back in the game, but Bowns and those in front put their bodies on the line to ensure it was a sweet start to what will be a hectic, long week.