The explosive winger won possession from left-back Joe Devera before speeding into the Bees box and firing in off the near post to give the Addicks the lead in what was a very close, see-saw affair at The Valley.
The visitors started off the brightest but soon found themselves under the cosh from some efficient Charlton passing and Reid's goal just shy of the 20-minute mark was, at the time, deserved.
However, the home side then spent the majority of the rest of the game fending off an admirable effort from the Football League's basement side.
Mark Stimson's men came close to forcing extra-time on numerous occasions, most notably with two one-on-one situations and a dynamite free-kick from ex-Addick Grant Basey, all of which were thwarted superbly by man-of-the-match Rob Elliot.
The Addicks will now go on to face Corby or Luton back at The Valley on Saturday November 27.