It was the Fleet's seventh home defeat in the Conference this season.
Gary Holloway had Aldershot's first effort on goal in the fourth minute when his shot from six yards was collected by brother Craig, the Fleet keeper.
Minutes later Fleet defender Ross Smith headed clear from under his own crossbar from a dangerous Leroy Griffiths cross.
With the Fleet looking to snap a run of only one win in eight games, the home side worked hard to take an early advantage. Bobby Bowry hooked a shot into Nikki Bull's arms and both Danny Slatter and Luke Moore had attempts narrowly off target in the first 15 minutes.
Liam Daish was forced into a strategic change after 19 minutes when Mark Rawle was stretchered off with an injury. Defender Robert Watkins replaced him and centre-back Jamie Smith pushed forward to try his luck as a striker.
The Shots' Ryan Williams was given plenty of room to run down the Fleet's right flank, and on 44 minutes he ghosted in behind a sleepy home defence to force the ball home from skipper Steve Watson's cross to put the visitors in front.
Williams needed less than a minute of the second half to double his tally. Straight from the kick-off he shuttled down the left wing before unleashing a blistering shot from outside the area, leaving Holloway without a chance of stopping it.
Worse was to come for the Fleet when, ten minutes later, their defence fell apart to allow Kirk Hudson to finish emphatically when he drilled the ball home from the edge of the box.
Gravesend tried to fight back and James Smith and Ashley Fuller both tried to spark a revival, but Bull's goal remained intact.