England struggled in the first-half and deservedly fell behind five minutes before the break.
But Callum Doyle of Manchester City equalised from a 52nd minute corner before both sides had chances to win the game in 90 minutes. Edwards made a couple of terrific blocks to thwart Isreal attacks.
Carney Chukwuemeka of Aston Villa bundled home a superb cross on 107 minutes to give England the lead and another Villa player Aaron Ramsey made the game safe four minutes from time.
Peterborough United's young stars shone to help secure a rare EFL Cup victory
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England won all five matches in the tournament and Edwards, the only player from outside the top two divisions of English football, played in four of them.
The last time the Young Lions tasted success in the U19 Euros, the squad which beat Portugal in the final included Mason Mount, Reece James and Aaron Ramsdale, all of whom have gone on to become senior internationals for England under Gareth Southgate.