Great Britain overturned a nine-point deficit late in the game to beat Israel 75-71 in overtime in their opening game of the EuroBasket in Slovenia.
Israel led 66-57 with less than three minutes remaining but Andrew Lawrence's free throw levelled the scores in the closing seconds of regular time.
Kyle Johnson then put Great Britain two points ahead and Andrew Sullivan sealed the win with two free throws.
Joe Prunty's team must finish in the top six to get next year's funding.
Johnson top scored with 22 points for Britain, who continue their campaign with a match against France on Thursday.
Captain Drew Sullivan told BBC Sport: "We stayed focused and gave ourselves opportunities to win the game.
"When you're down seven [points] with two minutes left and you make overtime... we were pleased. We were strong and on top and felt we were in the ascendancy.
"Our focus and goals haven't changed. We want to win every game. We have surpassed some people's expectations, but not yet our own."
UK Sport initially axed all support for the men's and women's basketball programmes in December, but then offered a conditional reprieve in February. For funding to extend beyond an initial 12 months, they were set the target of a top-six finish at the EuroBasket.