The visitors looked to be heading for a heavy defeat at the home of the defending English Premier Ice Hockey League champions as Flames raced into a 4-0 lead with 23 minutes on the clock.
But Bees refused to lie down and hit back with a hat-trick from Shaun Thompson as well as strikes from Martin Masa, Jan Bendik and Rob Lamey to seal a dramatic win.
It was the second thrilling victory of Bees' weekend after they beat Peterborough Phantoms 4-3 in overtime on Saturday.
Lukas Smital and Thompson put Bees 2-1 ahead in the opening period but despite a second goal for Smital, Phantoms forced overtime.
Masa ensured the overtime was short and sweet for the home fans, though, as he scored the winner with 73 seconds gone.
Bees are now third in the table, a point behind leaders Basingstoke Bison, ahead of a double header against Milton Keynes Lightning next weekend.
* SEE THIS WEEK'S NEWS FOR REPORTS AND REACTION FROM LAST WEEKEND.