Beckford put Huddersfield ahead in the 11th minute with a calm finish past Addicks keeper David Button to net his 16th goal in 19 appearances for four different clubs in the famous cup competition and delighting first-team coach Ian Miller.
"Jermaine can score goals. He's a natural goalscorer. I knew him from his time at Leeds and when he's smiling and happy, he's a threat," Miller said.
"Lately, he's just not had enough games due to injuries. But if you can get him and (Norwich City loanee) James Vaughan on the pitch they are a potent threat. The best in the Championship? I don't know.
"There's lots of teams spending mega money but they will certainly do for Huddersfield. They will both score goals."
Huddersfield now takes on Championship rivals Leicester City in the FA Cup fourth round at John Smith's Stadium later this month.