The first period saw the Brits hold a 12-7 advantage in shots on goal, but the goaltenders kept the teams off the board.
Slovenia drew first blood 6:53 into the second period and the Brits had plenty of opportunities to tie it up, but the Slovenes held the lead.
The Brits may have entered the third period down a goal in their first game after promotion, but they were not deterred, and after an early Slovenian penalty, tied the game 3:43 into the final frame.
The tie lasted all of 73 seconds, when the Brits pulled ahead. Slovenia tied the game midway through the period.
Neither team could break the tie in regulation, but the overtime period lasted only 37 seconds, as the Brits skated away with a victory.
“We know that we’ll have to win all of our other games if we want to finish first,” noted Subic. “Tomorrow will be a difficult game against [host team] France.”
Chruchfield and his teammates end the day in second place with two points while Subic and Team Slovenia sit in third with one point.