Harwich came close in the 8th minute when Freddy Bethell's shot hit the post and rebounded back into play.
Halstead came back but it was Harwich who took the lead with Jaidan Smith's cross being neatly converted by Ewan Livingston.
Midway through the half Halstead pressed and Shrimpers goalkeeper Matt Huggins advanced into his penalty area to make a serries of blocks from one attack. The visitors were enjoying a good spell and twice had efforts which struck the Harwich crossbar.
Harwich needed another goal and it came via a Darren Bethell free kick from which Harvey Smith netted with a glancing header to give his team a 2-0 interval lead.
Huggins was in action again in the early stages of the second half, turning a dangerous in-swinging corner kick over the crossbar.
It was nip and tuck now and it was Harwich's turn to be denied by the woodwork when Jaidan Smith's shot struck the upright.
Harwich were having to do well in defence to repel more pressure from Halstead and on occasions were thankful to Huggins, who was excellent acting a sweeper behind the high line which they were playing.
The Shrimpers came close to adding a third goal when the ball pinged around in the Halstead penalty area before being cleared off the goal-line.
With 25 minutes gone in the second half Halstead reduced the arrears when Huggins did well to push a shot out but had no chance when the ball was hammered back into the net.
Halstead now saw the chance of an equaliser but Harwich stood firm in defence and did have another scoring chance of their own when Freddy Bethell's snap shot went just over.
Harwich team: Matt Huggins, Tony Clarke, Solomon Griffths, Archie Corner, Alfie Robinson, Darren Bethell, Ewan Livingston, Harry Conway, Jaidan Smith, Freddy Bethell and Harvey Smith. Substitutes: Alex Pryke, Connor Humphreys, George Reid, Oscar Warnes and Henry Cross.