Whites suffered a second straight National League South defeat and a second defeat of the season as The Hawks maintained their unbeaten start to the campaign.
Muhammadu Faal turned home from close range to give his side the lead in the 16th minute before Alfie Pavey equalised against one of his former clubs nine minutes later.
Faal restored the lead from the penalty spot after Jake Goodman’s handball eight minutes before half-time.
Millwall loanee Ryan Sandford denied Faal from completing a hat-trick four minutes after the break when he saved his penalty.
However, just two minutes later, the hosts increased their lead when Jake McCarthy curled home past an unsighted Sandford.
James Roberts headed home to make it 4-1 in the 74th minute before second-half substitute, 18-year-old forward Noah Carney, reduced the deficit with his first senior goal five minutes from time.
The defeat sees Dover drop to 17th on the table ahead of Saturday’s game against Hemel Hempstead Town at Crabble.