Michael Rankine thumped the ball into the middle of the net from six yards after Craig Stanley's 56th minute cross deflected off several bodies in the box.
Moments earlier Shots keeper Jamie Young stood tall to block a one-on-one effort from Jake Reed, who beat the offside trap on the half-way line and ran the entire Aldershot half unchallenged.
Kieron Cadogan almost doubled the lead but his 76th minute shot from the edge of the area rolled across Chris Lewington's goal before going wide.
Josh Scott almost stole a point 10 minutes from time but overran Mo Shariff's low delivery into the six yard box.
Scott almost gave the visitors a late first-half lead by powerfully striking the ball towards the middle of the goal only for Young to instinctively block the effort before Scott hit the bar with the rebound.