It took the Tudors less than a minute to take the lead, Will Hoskins with his first goal for the club after the Hawks keeper could only parry David Moyo’s initial effort.
They thought they’d gone 2-0 up when James Kaloczi headed home from captain Jordan Parkes corner, but was judged to have pushed a player in the build-up.
However, Kaloczi got his goal in the 33rd minute when Alex Osborn broke down the right-hand side, crossing the ball in for a free header, Kaloczi giving the keeper no chance.
Soon after the break, it was three, Hoskins doubled his tally on the day and for the season when he tucked the ball past Whitehawk keeper Jordan Hawkins.
Substitute Matthew Campbell-Mhlophe got in on the action after 69 minutes, cutting inside and firing home from six yards, also his first goal for the Tudors.
Three minutes later the scoring was rounded off when Alex Osborn, smashing home from outside the area to make it 5-0 and secure the three points for the away side.
The win sees the Tudors climb into sixth place, but are only three points off top of the league Dartford with a game in hand. Whitehawk stay rock bottom, without a win all season, 17 points from safety after 21 games.
Elsewhere, Darnell Smith’s 28-day loan at Hungerford Town has expired and he is back with Barnet.