Johannah Leedham-Warner scored 22 points to lead Great Britain to a 90-87 overtime win against Israel in their first Eurobasket qualifying game.
GB only guaranteed overtime with 5.7 seconds left of regulation time, when Chantelle Handy hit a three-pointer.
Temi Fagbenle scored 19 points and Georgia Jones 14 as Great Britain edged the extra period with a late burst in a pulsating game in Manchester.
GB now travel to face group top seeds Greece in Wednesday's second qualifier.
Despite a strong start, Great Britain trailed 36-30 at half-time after scoring just two points in the last seven minutes of the half.
Coach Chem Buceta's half-time adjustments - favouring a smaller, faster line-up - gave GB the lead almost immediately after the restart as Leedham-Warner, Jones and Rachael Vanderwal hit threes.
Israel still had the advantage seven seconds from time, 77-74 before Handy, who scored 13 points in the game, rescued them with a three from some way back from the three-point line.
Israel again had the advantage in the extra period, leading 85-84 with 1:45 remaining before a pair of free throws from Jones, another pair from Vanderwal and a Leedham-Warner drive for two with 14 seconds remaining sealed a thrilling win.
Captain Stef Collins described the win as "definitely in the top five, for sure," in her 100-plus caps after Great Britain came out on top in overtime.
"You couldn't have scripted it any better," she said.