Harwich mounted an early attack with Leiston goalkeeper Marcus Mehew turning Jamie Eades header over the crossbar.
The Shrimpers then made the start that they were looking for when after 15 minutes play Luke Mayhew's powerful shot gave them the lead.
Harwich were on top but failed to build on their advantage and with 30 minutes gone Leiston came close to equalising with a shot that flashed across the goalmouth.
In the closing stages of the half Harwich threatened to score again when skipper Gareth Heath's pin point pass picked out Alfie Canning whose shot skimmed the post and again when Luke Mayhew's drive forced a good diving stop from Mehew.
At the start of the second half Mehew produced a great double save, firstly pushing out Canning's fierce shot and then stopping Mayhew's close range follow-up effort.
However Harwich were not to be denied and in the 60th minute scored a well worked second goal when Liam White set up Mayhew who neatly tucked the ball past the advancing Mehew. Harwich had stepped up the pace and ace goal getter Mayhew had a chance to complete his hat trick when a misplaced clearance fell to him but the Leiston defence did well to recover and block the danger.
Had not Marcus Mehew been in excellent form, Harwich would have had a runaway victory and the Leiston keeper again thwarted Mayhew with a fine diving save.
Liam White had been impressive on his return to the Harwich midfield and from Leo Carty's pass he deservedly scored the Shrimpers third goal.
Harwich Team: Brad Cook, Harry Tuck, Dan Keeble, Tyler Sullivan, Reece Harte, Gareth Heath, Liam White, Charlie Stoneley, Alfie Canning, Luke Mayhew and Jamie Eades. Substitutes Used: Alfie Smith, Leo Carty and Archie Corner.