A Robert Farmer goal just 15 seconds from the end of regulation was enough to seal a 2-2 draw against hosts Hungary and with it the point that was needed to see them finish top of Division 1A, earning them the right to face the likes of world giants like Canada, Sweden, Russia and Finland in 12 months time in Slovakia.
It will be the first time since 1994 that GB have played in the top tier and completes a remarkable achievement for a group of players written off by many before the tournament began and who only secured promotion from the third tier 12 months ago with a memorable gold medal in Belfast.
Ranked 24th in the world and the tournament's bottom seeds, GB were trailing the hosts at the Laszlo Papp Sportarena 2-0 with 10 minutes remaining.
But a goal from Sheffield Steelers' Rob Dowd halved the deficit and, following a penalty shot save from Rotherham-born netminder Ben Bowns, Farmer applied the magical touch when his effort to the front of the net somehow squirmed between the legs of Hungarian netminder Adam Vay and over the line.
It led to wild GB celebrations on the ice, on the bench and in a small section of the crowd, a total and understandable contrast with the stone-cold silence everywhere else in the arena as the hosts and the majority of the 8,000-strong crowd realised their own hopes of promotion to the top tier had suddenly vanished.
It still required some desperate defence in the dying seconds from Bowns and his team-mates but they held on and, after a goalless overtime, sealed an historic night for the British game when they won the match 3-2 on a shoot-out, a result which saw them finish two points clear of their rivals, with second-placed Italy joining them as the second promoted team.
"We dared to dream and we did it. I just cannot believe it," said head coach Russell. "This team is very special and what we have pulled off is absolutely unbelievable.
"We did not give up and showed true British spirit to pull that one out of the bag. I am so proud of every single one of them and we will now play the best teams in the world next year.
"Our team work rate was immense every single night and they dug need to provide GB with one of our greatest-ever moments."
The hosts went ahead on the powerplay at 3.31 when Christopher Bodo put a doorstep rebound past Bowns, who later had to be alert to make a glove save from Balint Magosi's shot before also denying Balazs Sebok.
A better performance was needed from GB after the first break and they found it, Steelers' Liam Kirk setting up Dallas Ehrhardt for a shot from left point that was well-saved by Vay. Dowd had two chances in quick succession, while Mark Richardson was also denied by Vay's pad from close range.
GB suffered the worst possible start to the third, Hungary going 2-0 ahead at 41.53 through a moment of good fortune when the puck cannoned in past Bowns after hitting Csanad Erdely's shoulder from a deflected pass, the goal eventually given after the kind of lengthy review from officials which had dogged the tournament throughout the week.
Paul Swindlehurst and Brett Perlini had chances to close the gap before, after a period of sustained pressure, Dowd spun and fired the puck through traffic on a rebound to reduce the arrears at 50.55.
Bowns saved his second penalty shot of the tournament to deny Janos Hari at 57.00 after he had been hooked by Farmer when presented with a one-on-one breakaway after a neutral zone giveaway by Steelers' Ben O'Connor.
But it still seemed as if GB would be denied a top two spot despite all their efforts until the energetic Farmer worked himself free on the left and fired the puck in front of net from where it deflected in off Vay's left pad.
After some understandably delirious on-ice celebrations and again at the end of regulation, GB's players then had to compose themselves for five minutes of overtime which, despite several chances at either end, stayed goalless.
Farmer then added a cheeky backhand effort in the shoot-out to seal his hero status, O'Connor scoring the other goal as Bowns completed a memorable week in net by making four saves at the other end.
Afterwards, Nottingham Panthers' match-winning hero Farmer joked that his historic goal was "rubbish."
"It is so hard to sum it up," said Farmer. "We are now going to play the best teams in the world next year and that is so amazing.
"It was a rubbish goal - but I just don't care. We never doubted ourselves and we dug deep to get the most breathtaking victory of my career."