Harwich gained the initiative in the early stages with a well-worked move when, from deep on the right flank, Alfie Canning crossed to the far post where Dylan Crowley (pictured) applied the finishing touch to give the Shrimpers the lead.
With 23 minutes gone. Harwich goalkeeper Jack Lines made a good save to keep his team in front but at half time the Shrimpers deserved their lead.
Crowley is enjoying a prolific scoring spell and within a couple of minutes of the restart his header went in just under the crossbar for his and the Shrimpers' second goal of the match.
Harwich continued to combine well and Stowmarket were also playing their part in an entertaining cup tie.
Stowmarket forced a series of corner kicks but the Shrimpers' back four were in commanding form and dealt with the threat.
After the match, the Harwich players were able to celebrate their victory - and their manager Luke Harrison's 40th birthday.