The visitors' two goals came during the first half through Tim Sills and Steve Watson.
The Shots went ahead on 15 minutes with their first chance of the game. From a throw in, Jon Challinor got the ball and raced to the byline before squaring the ball to give Sills the simple task of prodding home from three yards for his tenth goal of the season.
City struggled in midfield, missing Darren Dunning through a ban, and Leeds United loan player Rob Constable failed to perform in the midfield role.
York striker Andy Bishop showed fine skill in turning his marker on the edge of the box but his curling shot was at an easy height for keeper Nikki Bull.
As Aldershot took control, Chris Porter made a fine diving save to deny debut boy Martin Reeves with a diving header.
The Shots doubled their lead on 41 minutes following the award of a controversial corner. From a well-worked training ground routine, Watson was on hand to flick home the low angled cross from ten yards.
The game could have been over for York at half-time had Sills not missed with a header from point-blank range on 45 minutes.
Inside the first five minutes of the second half, the visitors had two further chances to increase their lead through Watson's header and Hugh McAuley's 20-yard drive, which came back off the post.
City then started to drive forward turning in a much improved performance in the second half.
Dave Merris got things going when he ran 40 yards into the box but Bull saved bravely at his feet. Then Kevin Donovan ghosted past three defenders but his cross-shot flashed wide.
The experienced Paul Groves turned in an excellent performance at the back but on 90 minutes, as his name was announced as man of the match, he almost headed into his own goal with a careless back header.