Having dominated the opening three periods, GB were outscored 29-13 in the final stanza but held on to take the victory and reach the last four for the first time.
Mary Durojaye led a balanced GB offence, which saw 11 players on the scoresheet, with 12 points and only missed a double-double by a single rebound.
Tamzin Barroilhet finished with 11 points and four boards, while Miari Buchan had ten points and five boards.
Ella Clark had five points to go with her nine rebounds and three blocks, while for Israel Naama Shafir led the way with 23 points.
GB out-rebounded the Israelis by an impressive 54-30 and finished with a better shooting percentage in all categories, but did turn the ball over 32 times.
GB started strongly in a game they led from tip to buzzer, with Durojaye opening the scoring before six straight Rebecca Allison points helped them open a 12-1 lead in the first six minutes.
Maytal Ovadia broke the run, but Charlotte Stoddart wrapped up the first period scoring from the foul line to send GB into the opening break with a 23-8 lead.
GB didn't let up and Barroilhet launched a 6-2 run to open the second period, and four straight points from the same player made it 33-11 with 5:32 on the clock.
Israel did stop the damage to a certain extent, but Renee Busch hit a jump shot to wrap up the second period scoring and send GB into the locker room with a 39-20 lead.
A Buchan lay-up made it a 21 point game 90 seconds into the third quarter, and although Idit Oryon sparked a 7-0 Israel line with a pair of foul shots, a Kristie Sheils trey put GB 48-29 ahead at the mid-point of the period.
Kashmere Joseph extended the lead, and her Barking Abbey team-mate Clark drained a trey off Allison's assist to get GB into the final break leading 59-36.
Eloisa Katz opened the fourth period scoring, and only Buchan troubled the scorers for GB in the first four and half minute as Israel cut the advantage to 16 points.
Sheils stopped the rot with a score from downtown, and when Katrin Chiemeka hit a jumper with 3:45 on the clock, GB looked home and dry with a 68-50 lead.
However, Israel proceeded to reel off 15 straight points capped by four from Shafir to make it 68-65 with 36 seconds remaining.
Barroilhet finally broke the run with a lay-up and hit the bonus after being fouled by Shafir, and Durojaye scored one from the foul line to seal the win and a place in the semi-final.
