David Syers nodded a dramatic late winner to lift City six points clear of the drop zone.
Syers struck in the 89th minute, nodding home a Gareth Evans corner for his tenth - and most important - goal of the season.
Omar Daley provided the perfect start for City with a thundering strike after just four minutes, his first goal since coming back from Rotherham.
In an eventful first half, James Hanson was the width of a post away from a second with an equally well-struck drive.
But Aldershot, who had lost only three in the last 18 games, came roaring back.
Twice they should have levelled as Peter Vincenti put a free header wide and then Alex Rodman hit the post when it looked far easier to score.
But City's uncertain defence was punished three minutes before the break as Vincenti fired home after Rodman's initial shot had been blocked.
The second half was a bitty affair but Young pulled off a fine save to deny Robbie Threlfall.
Then, with time ticking away, Syers popped up in a scrum of players to convert a late corner and surely ensure City will still be in League Two next season.
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