Harriett Yea (13) and Stef Collins (11) were also in double figures as Mark Clark"s team completed a good all-round night. For Bosnia, Natasa Mikic led the way with a game-high 27points.
The Bosnians won the tip, but saw Stupar Anja"s effort blocked by Collins, and it was the hosts who opened the scoring on 9:19 when Rose Mason drained a jump shot as the shot clock wound down.
The visitors levelled, but Collins drained a three and Mason scored from close range to put Britain 7-2 ahead. The visitors reply saw them hit six straight points "€Â" split by a time-out from GB coach Mark Clark "€Â" to lead 8-7 with three minutes gone.
A Butler 15 foot jump-shot after a long GB possession put GB 9-8 up, but Butler was called for a foul on Anja who hit one from two charity shots to level the score at 9.
Kristy Lavin entered the action just before the midway stage of the quarter, and drained a three within 15 seconds before Mason converted an old fashioned three point play to see Britain go 15-9 ahead with 4:02 on the clock "€Â" and they never trailed again.
A Mason steal and lay-up with 2:02 on the clock put GB 17-9 ahead, forcing a time-out from the visitors, and that lead was extended to 11 as Butler converted an and-one.
The lead continued to grow as Collins drove to the basket and laid the ball up, and Lavin converted a pair of free-throws to put Britain 24-14 ahead with 10.5 seconds remaining.
As Bosnia looked for the final shot, Mason did well to steal the ball and fed it to Collins to drain a buzzer beater to send Britain into the first break 26-14 ahead.
Bosnia opened the second period with a 7-3 run "€Â" Harriet Yea draining from downtown for GB"s score "€Â" before a Mason shot broke the tear and took her tally to 11.
Yea again scored from long range to put Britain 34-21 up with three second period minutes gone before Butler converted a lay-up off Collins" assist.
Barking Abbey player Yea again scored from the Land of Plenty to put Britain 39-21 ahead with 5:49 on the clock after force another timeout from the visitors.
Single free-throws from Butters and Butler saw the British lead grow to 41-21 before Clark called another timeout with 3:23 remaining, before Bosnia finally ended their drought with a Samra Omer lay-up.
Lavin replied with a trey and Butler converted a Hutchinson assist to put GB 46-23 ahead with two minutes remaining, and Britain closed the half out to lead 50-25 with Mason leading the way on 13 points and Butler (10), Yea (9) and Lavin (8) all contributing well.
Meagan Hoffman"s "and-one"€ launched the second half with Metesa Tavic reply ing two minutes later as both sides struggled top trouble the scorers.
Hutchinson converted an and-one after a good steal from Collins as the British lead grew to 56-28 at the 6:37 mark and although the visitors replied with five straight points, Butler broke the tear to make the score 59-33.
A 7-2 Bosnian run cut Britain"s lead to 21, but Collins drained a pair from the charity stripe as the visitors" physical play saw them continue to chalk up the fouls, and Clark called another time-out with Britain 63-42 ahead and 2:32 in the third period remaining.
The visitors cut that lead to 16 with exactly a minute left in the period forcing a triple substitution from Clark, but an sportsmanlike foul on Tavic as she hammered Hutchinson saw the Auguere player convert the bonus and Butler scored from close range after another Mason assist to end the tear and put Britain 68-47 ahead going into the final break.
Lavin drained a trey off a Hutchinson trey to open the fourth period and Mason converted a lay-up as the shock clock ticked down to give Britain a game-high 26 point lead.
An excellent in-bounds play saw Butler lay the ball in, and with Mason making in 77-47 with eight minutes to play, the game was effectively over.
Butters fouled out on an offensive call with 3:05 remaining and GB 82-53 ahead before Yea drained her fourth trey of the game and a Collins lay-up with 1:21 on the clock to the lead up to 33 to wrap up the win.
