The match was devoid of goal-scoring opportunities after Ricky Holmes had cleared Ollie Lancashire's header off the line in the opening exchanges. But Reid's 68th-minute strike ensured Aldershot ended their poor run of form and increased the early-season pressure on Bees' boss Mark Robson, whose side remain rock bottom.
Lancashire nearly put the hosts into a seventh-minute lead with his headed effort but both teams struggled to impose themselves.
Danny Hylton, returning from an eight-match ban, was full of running but other than Bees full-back Jordan Brown's saved effort, neither team created much in the first-half.
John Oster's shot from distance 20 minutes after the break was the second half's first effort in anger but just five minutes later Aldershot took the lead through Reid's sliding finish.
A goalmouth scramble after 77 minutes nearly doubled the home side's lead as Barnet's challenge petered out and the Shots secured their first home win of the campaign.