There was a first-minute scare for Harwich when Hackney Wick tried a shot from the halfway line that dipped an inch over the crossbar.
The Wick followed this up with 10 minutes of fast and frantic football that had Harwich on their toes to compete with them.
Having come to terms with this start, Harwich took the lead when Alfie Eldridge was brought down making a run on goal and Jake Gordon (pictured) hammered home the resultant penalty kick.
With 18 minutes gone, Mason Rees equalised for Hackney Wick direct from a corner.
Gordon was leading the Shrimpers' attack for the first time since his arrival at the club and from his long, raking pass, Josh Hawkins did well to force a dangerous corner kick.
Harwich regained the lead from a move started by Jenson Goode that saw Rory Harman fire in a pin-point cross that was headed into the net by the well-placed Gordon to score his second goal of his Shrimpers career.
Ten minutes into the second half, Harwich came close to scoring again when an Eldridge shot was cleared off the goal-line.

'England Day' coming to Royal Oak!

Midway through the half, the livewire Eldridge was brought down again when in a clear goal-scoring position and this time the Hackney Wick player was dismissed. Wick goalkeeper Tyron Osadolor did exceptionally well to dive and get his hand to the powerful penalty kick that followed but could not prevent the ball entering the net and Shrimpers striker Gordon completed his hat-trick.
It was proving a memorable display by Harwich and, with 10 minutes remaining, Tiwa Odufuye scored from close range to increase their lead to 4-1.
Full marks must go to Shrimpers joint managers Matt Carmichael and Sean Tynan, who had got their team selection and tactics spot-on for this match and have also assembled a strong squad, who look capable of climbing the league table.
In injury time, Louie Bloom put the icing on the cake when, from a wide position, he scored Harwich's fifth goal.
Harwich had taken a strong following of supporters to the match staged at Witham Town's stadium and at the final whistle they applauded their team off the pitch.
Harwich team: Will Healy, Rory Harman, Charlie Canham, Lewis Wood, Jeremiah Ajisafe, Jenson Goode, Josh Hawkins, Alfie Eldridge, Louie Bloom, Joe Knight and Jake Gordon. Substitutes: Alfie Canning, Oakley McNair, Liam White, Tiwa Odufuye and Tobi Dehinsilu (all used).