Dean Cracknell fired the Ryman Premier League side in front with an unstoppable 30-yard volley in the first half. But Shots striker Hylton headed home Kieron Cadogan's cross on the hour before tapping home an 85th-minute winner to help the hosts avoid a replay at Vale Farm.
Aldershot were the first to threaten, as Berkley Laurencin reacted smartly to repel Craig Reid's close-range strike, before Peter Vincenti thundered the rebound against the upright.
But the Shots were soon counting the cost of their missed chances as the visitors took an improbable lead on the half-hour mark courtesy of former Northampton trainee Cracknell.
It should have got worse for the hosts but Elliott Brathwaite fluffed his lines, heading wide from a Michael Murray corner.
The Shots eventually restored parity in the 57th minute as Hylton stooped to angle Cadogan's cross back past Laurencin. The equaliser prompted an onslaught from the hosts and Hylton duly broke Hendon hearts with his late winner.