Despite dominating the second half, the Shots were unable to break the deadlock and were forced to settle for a point after an impressive second-half display from Plymouth goalkeeper Jake Cole.
Hylton was left red-faced after missing a glorious opportunity to put Aldershot ahead on 27 minutes from the penalty spot. Cole saved Hylton’s placed strike after Paul Bignot had needlessly conceded the penalty.
The Pilgrims are unbeaten in their last four league games, and it was easy to see why as Ross Worner was called upon to save brilliantly from Nick Chadwick just past the half hour.
Hylton was again holding his head in his hands on 38 minutes as he headed inches wide as Aldershot attempted to turn the screw before the break.
With two minutes remaining Aldershot thought they had snatched victory as Hylton fed substitute Charlie Henry in the penalty area, but his effort was palmed away by the impressive Cole as Plymouth hung on.