Bradford-born Brown, 17, went on to enjoy a five-point night in the Division II Group A encounter in Tallinn, as Tony Hand’s team came back from going behind to a fourth-minute opener from Australia’s Michael Riley to dominate their second game of the tournament.
Moments after shooting just wide, Brown equalised for GB when he stepped out from behind the net and fired into the roof of the net across netminder James Downie at 14.15. Less than two minutes later, Britain were ahead after Cade Neilson put away a rebound at 16.08 for lead his team took into the first period break.
Brown scored his second of the afternoon 15 seconds into the second period on a rebound from Kirk’s shot before turning provider to set-up his Elite League team-mate Kirk for his first goal of the tournament at 24.10.
Just 23 more seconds had elapsed when Kirk scored his second, before great work from Mason Alderson-Biddulph freed Neilson for his second at 28.08 while GB were short-handed.
On the same powerplay - and just 10 seconds later - Australia grabbed their second through Kale Costa, before Brown completed a memorable treble when racing clear to fire past Downie at 34.13.
Alderson-Biddulph broke free and fired low from the left circle for GB’s eighth two minutes into the third period, before Jordan Buesa struck at 47.25 to complete an impressive victory.
“We did a good job again,” said interim head coach, Hand. “I thought we started off a bit slow, but we changed a few things up.
“Once we got going we really found our stride. They are young guys and they are still developing. We have 12 first-year guys on the team but everyone is doing really well and we are happy with the first two games.”
GB return to action on Wednesday when they face Poland at 1pm (11am UK time).