Jack Strange's fourth-minute goal was enough to give title-chasing Horsham the points in a dour, but hard-fought contest on Non-League Day.
In front of a superb crowd of 1,577, Strange met a corner to give the Hornets the lead that they never really looked like relinquishing.
Although Hendon defended reasonably well in spells, they struggled to create anything tangible in the final third as the home side held out for the 1-0 win.
The Greens remain 7 points from safety with six matches remaining, beginning with next Saturday's visit to Canvey Island.