Kazaiah Sterling and skipper Cameron Carter-Vickers put us 2-0 up in the first half but, after Harry Panayiotou halved our lead just before the interval, Leicester substitute Keanan King levelled within two minutes of the start of the second half.
A brace from Kenny McEvoy then saw us re-establish a two-goal advantage, but back came the Foxes once more as Elliott Moore and Panayiotou evened it up at 4-4.
We responded quickly, though, and after Shayon Harrison's well-taken half-volley, the same player scored from the penalty spot after Emmanuel Sonupe was hauled down by Alie Sesay.
Filip Lesniak then netted his first ever Barclays Under-21 Premier League goal to round off a remarkable victory in the rain at the Training Centre.
Spurs U21s: Whiteman, Walker-Peters, Amos, Lesniak, Carter-Vickers (c), Maghoma, McEvoy (Sonupe 70), Walkes, Sterling (Veljkovic 67), Harrison, Georgiou (Goddard 80). Substitute (not used): McDermott (GK).
Leicester City U21s: Maddison, Miles, Sesay (c), Chaudhury (Barnes 73), Moore (Olukanmi 73), Davis, Ndukwu, Cain, Panayiotou, Barmby, Fox (King 46). Substitutes (not used): Kipre, Bramley (GK).
Above: Cameron Carter-Vickers wins a header.