Neither side were able to take control of proceedings in the opening exchanges, but the game soon exploded into life just after the 22-minute mark, as Israel asked questions of the Young Lions' defence.
PSV starlet Tai Abed was barely an inch away from getting a toe on the ball to poke home the opener, and Jarell Quansah was called into action to quell an incisive Israel attack before the pressure of Ofir Haim's side paid dividends.
Some nifty footwork from Gloch inside the area beat the England defence all ends up, and the 18-year-old fired home past Brentford's Matthew Cox to hand Israel a deserved advantage.
Dane Scarlett could not take advantage of a goalkeeping gaffe from Tomer Tzarfati just before the break, but England were back on level terms in the 52nd minute, as Doyle was in the right place at the right time to finish from close range following a corner.
Ian Foster's side demonstrated a marked improvement after the restart, and a driving run from Quansah ended with Ramsey firing a low effort into Tzarfati's clutches, but the England defence had to be on hand to block Abed's drive immediately after.
England began to turn the screw with 10 minutes left on the clock, as Aston Villa starlet Chukwuemeka rattled the woodwork with a deft strike before firing another effort just wide of Tzarfati's post.
Cox was also called into action, diving down low to keep out Idan Gorno's header, but neither side could find the breakthrough before the extra-time period commenced.
After coming so close yet so far to making the net ripple in normal time, Chukwuemeka made no mistake in the 108th minute, darting into space to meet Harvey Vale's perfectly-weighted cross and bundle the ball home off his thigh.
Israel so nearly hit straight back through Gloch, but Doyle was on hand to preserve England's lead, which was doubled in the 115th minute to put the result beyond any doubt.
Tzarfati could only parry Liam Delap's shot into the path of Ramsey, and the Aston Villa man finished with aplomb to seal the deal for the Young Lions, who avoided any shocks in the final few moments to spark wild celebrations.