The Essex side dominated the opening half with on loan Braintree Town striker Jordan Cox scoring twice after 16 and 20 minutes and Leiston keeper Ashlee Jones also saving a penalty.
After Tom Derry added a third goal three minutes into the second half, Jack Ainsley opened his Blues account, firing home on 66 minutes after seeing his spot-kick saved.
Any chances of a late revival were dashed when Derry scored his second goal of the night and the hosts fourth with six minutes remaining.
Ryman League
Grays Athletic`s top five hopes took a blow when they were held to a goalless draw at Bloomfields by lowly Needham Market.
Tuesday`s only other game to survive saw the Metropolitan Police move up to twelfth spot after edging out Harrow Borough by the odd goal in five at Imber Court.
Tom Hickey gave the Met a great start with a goal inside the opening minute. And it got even better for Jim Cooper`s side when Joe Turner added a second just two minutes later. And a real hammering threatened when Andre Da Costa made it 3-0 with only eight minutes gone on the clock.
But Harrow settled and held the score to 3-0 at the break and then threatened more in the second period. And in the end the Met were made to sweat when Spencer McCall scored twice in stoppage time.
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