Striker Marvin Morgan scored an 86th-minute winner for Aldershot following an outstanding display by Shots goalkeeper Jamie Young.
Morgan latched on to a through ball to slot home past advancing goalkeeper Scott Bevan after Aldershot had weathered a second-half storm from the home side.
Young made superb saves to deny Eunan O'Kane and Chris Zebroski as the Gulls tried to break the deadlock.
He pulled off a spectacular diving stop to tip away O'Kane's goalbound drive and then denied Zebroski as the striker let fly from just inside the box on the right.
The visitors hit the woodwork in the 82nd minute when a cross-cum-shot from Anthony Straker from the left came back off the angle, before Morgan`s dramatic winner.
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