The 18-year-old, who has just agreed a new, two-year deal with Sheffield Steelers after completing his apprenticeship, hit the game-winning goal with less than two minutes remaining to secure a 5-4 victory and get Martin Grubb's side up and running at the third attempt in Division I Group B in Szekesfehervar.
The victory was hard-earned, particularly coming on the back of defeats to Slovenia and Japan.
Head coach, Martin Grubb was delighted with his team's efforts as he now prepares them to face Austria on Friday morning.
"I thought we started really well and when we were five-on-five, we were dominating the game as we have in most games," said Grubb.
"We got ourselves ahead in a good position and we were good on the powerplay with three goals, but then we took too many penalties and it started to cost us again.
"We then showed what huge character we have in this group and made sure we found a way to win tonight and the boys deserve the credit they receive."
GB took the lead on the powerplay through Sam Talbot at 4.48, only for Hungary to his back just seven minutes later when Balazs Varga found a way past Lucas Brine. Brown then got in on the act with his first when, after winning the puck in his own zone, he accelerated away to score on his backhand at 17.18.
Grubb's youngsters then took full control of the game when they scored two powerplay goals in just 42 seconds, the first from Brown when he hit home a rebound at 24.35 after Joe Hazeldine's initial effort had been saved. Bradley Bowering then made it 4-1 when he scored from close-range.
The hosts gave themselves hope at 36.32, however, when Adam Szucs scored from the left circle after the puck had bounced back off the backboards.
That goal gave Hungary fresh legs and they levelled the clash with two powerplay goals of their own in the third, the first from Gergo Ambrus at 45.59 after a scramble in front of net before Mark Schlekmann forced home a rebound at 49.52.
Brine then kept the game all-square with a number of quality saves which allowed Brown to display a sense of perfect timing when completing his hat-trick with the game-winner at 58.08 when he fired home from Mason Alderson's backhand feed.