Hammond (pictured, right, by Gavin Ellis/TGS Photo) scored after 21, 24, 39 and 77 minutes as Harlow strolled to a 4-0 victory.
The result lifted Harlow a couple of places up the table, to 17th, and meant that there is a six-point gap between Brentwood, the new 19th-placed team, and Ilford in 20th.
Ilford, who are above Redbridge on goal difference, had hopes of staying in touch with the sides above them after Usama Hamdan gave them a shock half-time lead at Grays.
Ryan Kirby equalised two minutes after the break and Junior Baker netted after 72 minutes to give Grays a 2-1 win which lifted them to third place.
Ware stayed four points adrift at the bottom after going down 4-1 at Witham, who moved into the top half of the table. Two quick goals from John Watson and Jason Fontaine midway through the first half put Witham in charge.
David Hunt gave Ware hope three minutes after the interval and only 12 minutes were left when Rob Whitnell restored the two-goal gap. Then Watson struck again to make quite sure.
Keep up-to-date with our exclusive email newsletters.
Subscribe