On their all-weather surface, Sudbury took the lead in the 10th minute when they mounted an attack that forced Shrimpers goalkeeper Brad Cook to advance and Jed Jackson found the net with a clinical finish.
Midway through the half, Harwich equalised when goalkeeper Kasey Clark was unable to deal with midfielder Alfie Eldridge's 25-yard shot.
However, Harwich were finding it difficult to cope with the speed and accuracy of Sudbury's game in midfield and attack and in the 30th minute Sudbury's touchline-hugging winger Sam Cox was left unmarked and from his cross to the far post, it was easy for Luke Mallinson to restore the home team's lead.
Harwich were unlucky when they had an effort strike the upright but Sudbury continued to be the better team and increased their lead with a super goal from Luca Terminiello, who skilfully created space before rocketing his shot past Cook.
Joe Knight broke clean through the Sudbury defence and it seemed that the Shrimpers' ace marksman would score but this time his shot went the wrong side of the post.
On the evidence of this half, a two-goal deficit was a mountain for Harwich to climb, but after the break they came out determined to put pressure on the Sudbury youngsters. Harwich were creating numerous scoring chances but goalkeeper Clark produced some excellent saves to keep his team in front.
Shrimpers boss Matt Carmichael used his substitutes, with Danny Garrad coming on and bringing an added impetus to their attack and he provided the opening from which Alfie Canning reduced Sudbury's lead to a single goal.
Harwich had the initiative now and it seemed that, with enough time remaining, they could rescue the points.
However, it was not to be when Sudbury broke away to restore their two-goal lead and break the Shrimpers' hearts.
Striker Joe Knight had worked desperately hard throughout and on another evening could have netted a hatful of goals, but with 5 minutes remaining Harwich suffered another blow when he received a second yellow card and was sent off.
He will now miss the home game with Dussindale on April 19, a match which has now taken on added significance.
Although the runners-up spot remains in their own hands, Harwich may well need to win all three of their remaining games in order to secure second spot. First, they will be keen to recover from this loss and lock in a home play-off semi-final - they still require five points to do that, as things stand.
Harwich team: Brad Cook, Oakley McNair, Jack Wood, Dan Keeble, Reece Harte, Alfie Eldridge, Gareth Heath, Liam White, Alfie Canning, Luke Spurling and Joe Knight. Substitutes: Danny Garrad, Louie Bloom, Alfie Smith, Tyler Sullivan and Keelan Milburn (all used)