The wide man was alert to pounce on rebounded shots from Phoenix Patterson twice inside 12 minutes as we made a bright start at the Foxes' training ground.
Khanya Leshabela halved our lead from the penalty spot midway through the second period but we survived some late pressure with Jonathan De Bie pulling off an important save and Leicester's Morgan Brown hitting the post to ensure we got off to a winning start in Group E of the new competition.
We were on the front foot straight away and after Patterson hit the post inside two minutes, Markanday was there to fire us ahead.
It was 2-0 just 10 minutes later as again Patterson got a shot away, this time goalkeeper Jakub Stolarczyk was in the way of it but Markanday once more tucked away the rebound.
Moments later, Stolarczyk made a double save from Brooklyn Lyons-Foster and then Markanday, while De Bie saved well from Conor Tee on 33 minutes.
Leicester found a way back into the game on 68 minutes when full-back Matt Lock was penalised for a challenge on Leshabela and the same player scored the resulting penalty.
Rodel Richards did well to adjust his body and test Stolarczyk at the other end on 81 minutes, while Markanday might have had his hat-trick when Maurizio Pochettino played him through on the break, but Stolarczyk spread himself well to block.
Leicester pushed us back late on and after De Bie saved from Tyrese Shade, Brown saw his header hit the post three minutes from time. Thankfully, though, we managed to see out the win.
Spurs U18s: De Bie (c), Lock, Reynolds, Bowden, Statham (Omolabi 73), Lyons-Foster, Patterson (Mukendi 69), P Maghoma, Richards (Pochettino 83), A Shashoua, Markanday. Substitutes (not used): Tainio, Oluwayemi (GK).
We return to Under-18 Premier League action at home next Saturday when Aston Villa are our visitors for a 12noon kick-off.