The Green and Whites had to make do with a four try bonus point after indiscipline saw their visitors profit from penalties in their 35-27 victory.
The hosts outscored their opponents four tries to two, but Dartfordians' Will Peters kicked 18 points from penalties.
That added to two conversions and a drop goal gave the London side - who played the final ten minutes with fourteen men - a narrow win.
Horsham remain sixth with the point as another well-contested encounter played out between the two sides.
Peters put the visitors ahead with an early penalty, but Horsham hit back as a lapse in the Darts defence saw Jordan Smith go over, with Will Bell converting.
The kicker added a penalty of his own soon after, but back at the other end, as the Horsham penalty count stacked up, Jake Taylor went over from a line-out. Peters levelled the scores at 10-10 by adding the extra and then a further two penalties to lead 16-10 at the break.
A Will Johnson try pulled it back to 16-15 early in the second half, before the visitors raced into a 29-15 lead as Liam Brencher put down a converted try. An Ollie Harcus score moved the scores to within nine points before Brencher was shown a red card for illegal use of the boot.
Despite this Dartfordians put over another two penalties and although Andy Gray crossed the try line with the final play of the game with Bell converting, a bonus point was as good as it got for Horsham.
The Green and Whites travel to Dulwich based Old Alleynians on Saturday in the league to face a team who sit a place below them in seventh.
Horsham: Plane, Fisher, Barber, Harcus, Clarkson, Smith, N Bell, Whiting, J Johnson, W Bell, Wilson. Carvell, J Bell, Gonzague, W Johnson. Subs: Gray, Tredgett
Report by Ollie Berry, WSCT