The Shrimpers had an early chance when Zac Pedro's cross found Louie Bloom, whose header went close.
The Rovers took the lead in the 16th minute when, from a cross, Thomas Barton's powerful header gave goalkeeper Brad Cook (pictured) no chance.
Harwich striker Joe Knight twice tried long-range shots which went over the crossbar.
However, Great Wakering finished the half on top and just before half time their impressive leader, Luke Hirst, converted a cross, firing in their second goal at the near post.
Harwich faced a mountain to climb when, soon after the start of the second half, Hirst burst through the home defence and powered his shot through Cook's legs.

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Against such good opposition, there was no way back for the Shrimpers, although they might have reduced the arrears in a couple of skirmishes in the Rovers goalmouth.
In the final minute, Rovers netted their fourth goal from a low, well-struck drive from Shaun Gittleson that nestled neatly in the corner of the net.
It was Harwich's third defeat in a row and they remain in the middle of a difficult run of fixtures against teams in the promotion race. On Saturday they face third-placed Barking, then SOUL Tower Hamlets and Little Oakley, who both have games in hand that could take them into the automatic promotion spot.
Harwich team: Brad Cook, Tom Watkins, Charlie Canham, Jack Wood (captain), Tiwa Odufuye, Jenson Goode, Liam White, Alfie Canning, Louie Bloom, Zac Pedro and Joe Knight, Substitutes: Reuben Keeys, Oakley McNair, Luke Hopwood and Luke Mayhew (all used).