South Division leaders Hadleigh United were the first to create a scoring opportunity but a timely tackle by full-back Oscar Warnes snuffed out the danger.
Harwich took the lead in the 10th minute when Danny Garrad broke through the home defence and set up Ewan Livingston (pictured, left), who netted with a neat finish.
With 20 minutes gone, the Shrimpers scored their second goal with a carbon copy of the move and this time it was Livingston who was provider, for Garrad to apply the clinical final touch.
United are a smart outfit and reduced the arrears when Alex Spraggons netted at the far post.
It was proving an exciting cup tie and Shrimpers goalkeeper Thomas Maurer was twice in action, punching out a free kick and later doing well to come out and dive to smoother the ball when a goal looked certain.
After the half-time break Harwich had a goal ruled out by the linesman's offside flag but scored an all-important 3rd goal when Liam White played the ball through to Jack Milne, who beat the keeper with a smart shot.
Hadleigh's hopes of a second comeback were dented when a second yellow card reduced them to 10 men and although they kept trying, the Harwich defence was in good form.
The icing on the cake came for Harwich when an effort from Cody Harrison struck the crossbar and rebounded back into play for Garrad to head in his second goal.
Harwich now entertain North Division leaders, Framlingham Town, this coming Tuesday (25th February), kick off 7.45pm, in what has all the makings of a thrilling encounter.
The Shrimpers will be hoping for a bumper crowd of supporters to cheer them on in their efforts to reach the final where Brantham Athletic await.