Goals either side of half-time from Rochdale's top-scorer Ashley Grimes and Shots striker Michael Rankine, his third of the season, looked like sending the game to extra-time.
But striker Hylton grabbed his fifth of the season with a sublime volley 12 minutes from time to send Aldershot, the lowest-ranked side left in the competition, through to the next round.
Grimes almost opened the scoring in the first minute but had to wait until just before half-time to do so, grabbing his sixth of the season with a neat finish.
But moments after the restart the home side were level, Rankine equalising with a superb overhead kick as Dean Holdsworth's men looked to extend their unbeaten run to eight games.
The Shots had already beaten West Ham and Carlisle to get this far and Hylton made sure the run continued, ending Rochdale's best Carling Cup run since 1962 with an unstoppable effort into the top corner.