The jubilation was in part due to the fact that the final margin somewhat flattered the home team who found themselves locked into a titanic struggle with the visitors until a blistering final period.
Ukraine finally fell apart and were blown away 26-12 by the group leaders who remain unbeaten thanks to another scintillating performance by Luol Deng who poured in 28 points to go with his seven rebounds and four assists.
After a sluggish start, a three-pointer by the in-form Dan Clark tied things up at 10-10 as he continued his flawless shooting from the previous game in Bosnia and Herzegovina when he was five of five from the arc.
Moments later he threw down a big dunk and it was a good job with Ukraine lighting it up from outside. That proved to be the foundation for a real scoring surge which had Great Britain on the ropes and trailing 38-26.
However a flurry of triples in quick succession by Ogooluwa Adegboye and Nate Reinking formed the basis for a 15-2 run to change the momentum and hand them the lead once more at 41-40.
Great Britain still held on to a one point lead at the half and at 64-64, the game was delicately poised.
However much to the delight of the home fans, Chris Finch's team put their foot on the gas and really picked up their game. With Deng instrumental in everything good at both ends of the floor, it was his three-pointer and spectacular dunk in the closing minutes which finally killed off the gutsy visitors.
Clark and Pops Mensah-Bonsu both played important cameo roles to Deng. Estudiantes forward Clark had 13 points and nine rebounds while new Caja Laboral acquisition Mensah-Bonsu finished with 15 points and eight rebounds.
Maksym Pustozvonov top scored for Ukraine with 18 points.
"It was really similar to all of our performances and we're in an excellent position as we're 4 and 0. But as I said to the guys it's important to keep it in context, we're winning the games in the last four minutes and there's not much margin for error. I'm really proud of the guys, they're out there giving 100 percent, playing a lot of minutes and making the big plays down the stretch. We dug deep, and the guys stepped up in the final minutes. Dan Clark's been hugely instrumental in our success to date, he doesn't draw a lot of attention but he's got a great basketball IQ, he passes well, rebounds well and made huge step forward from last year. This team suits him a little better than last year, and he's seized the opportunity."
Great Britain player Andrew Sullivan:
"It was an ugly game but when you go out there you try to win regardless of how it happens. We set goals for ourselves, but if we have to win ugly so be it."
Ukraine coach Vitaliy Cherniy:
"In the first three quarters we played some very smart, good basketball, and we played the game how we should. But in the final four minutes we played awful, too many stupid mistakes and that's why we lost."
Ukraine player Maksym Pustozvonov:
"It was really hard to play in the gym it was big and the supporters were unbelievable plus it's always hard to play away from home. GB have a good team with some high level players and like our coach said we played some pretty good basketball until the final few minutes of the game. We will try to improve for the next game."