The Lions were leapfrogged into third by Preston Nomads CC, who recorded a 77-run win at home to Bognor Regis CC.
Opener Ollie Haines top-scored for Horsham with 81 while skipper Nick Oxley and Will Beer added healthy contributions of 41 and 39 respectively.
The Lions looked in control at 217-4 but a flurry of late wickets from the excellent Rowan Naude (5-72) and Ollie Blandford (2-45) restricted the hosts to 245-9 off 53 overs.
Bridges faltered in their reply, falling to 38-3, but a 77-run fourth-wicket partnership between Thorn Parkes (38) and captain Joe Walker (51) steadied the ship.
Parkes and Walker were eventually dismissed by Bertie Foreman (3-78) and Beer (2-41) respectively and Bridges’ momentum slowed.
Luke Bellars (31) and Arran Brown (35 not out) made good scores but the run-rate had got away from the visitors.
The game ended in a draw with Horsham needing three more wickets and Bridges 43 runs short.
The Lions travel to bottom-of-the-table Eastbourne CC this Saturday, while Three Bridges host second-from-bottom Mayfield CC.
Here is a selection of photos from the game courtesy of photographer John Lines.
1. Horsham slip to fourth in the Premier Division after Three Bridges draw - the match in 33 pictures
Action from Horsham v Three Bridges Photo: John Lines
2. Horsham slip to fourth in the Premier Division after Three Bridges draw - the match in 33 pictures
Action from Horsham v Three Bridges Photo: John Lines
3. Horsham slip to fourth in the Premier Division after Three Bridges draw - the match in 33 pictures
Action from Horsham v Three Bridges Photo: John Lines
4. Horsham slip to fourth in the Premier Division after Three Bridges draw - the match in 33 pictures
Action from Horsham v Three Bridges Photo: John Lines