In the first minute, Harwich created a chance from which Alfie Canning's header went the wrong side of the post.
Harwich continued to play at a high tempo and were competing well for every ball.
With 30 minutes gone, Halstead threatened but good defending by Harwich saw the shot diverted for a corner kick.
Harwich had another good opportunity from Canning's well-directed free kick but Zac Pedro could not get his shot on target.
Louie Bloom was leading the Shrimpers' attack and in the goal area, his acrobatic shot was blocked at the expense of a corner.
Canning was prominent in the Harwich midfield and he made a lightning run on goal, only to be brought down, with the Town defender receiving a yellow card.
With a minute to go to half time, somewhat against the run of play, Town took the lead when striker George Smith hooked his shot into the net.
Ten minutes after the restart, Liam White played a clever through pass to Tiwa Odufuye (pictured). He planted the ball neatly in the Town net but had strayed marginally offside.
Pedro crossed the ball accurately for Odufuye, this time onside, to head goalward, but Josh Woodrow, in the home goal, pulled off a good diving catch.
Halstead were using their physical advantage to gain control of midfield, and with Harwich losing their shape, the home side were dangerous from a series of corner kicks.
With 58 minutes on the clock, Shrimpers centre half Charlie Canham was adjudged to have gone over the top of his opponent to win a header, and from the resultant free kick, Smith headed his and Town's second goal.
With Town now in the ascendancy, it was an uphill battle for the Shrimpers to try to get back in the game.
Following a free kick, Canham went close with a snap shot that went over the bar.
In the 75th minute Harwich had a chance to reduce the arrears Bloom was through but Woodrow did well to block his shot and the striker's second attempt went over the crossbar.
Halstead were getting their big players forward for set pieces to try to make their aerial superiority count, keeping the Harwich defence at full stretch.
White had a well-struck 20-yard drive touched out for a corner kick which was scrambled away for another corner and Harwich hopes of a late comeback were gone.
Special thanks to our good friends at Halstead Town Football Club for their excellent hospitality and our best wishes for the remainder of the season.
Harwich team: Brad Cook, Jack Cosby, Charlie Canham, Oakley McNair, Reece Harte, Jenson Goode, Alfie Canning (captain), Zachary Pedro, Liam White, Tiwa Odufuye and Louie Bloom. Substitutes: Mo Hashemi, Josh Beavis and Luke Hopwood (all used).