The hosts touched down two late tries to grab the win, although Raiders returned home with two points - a four-try bonus point and a losing bonus point.
Raiders led 26-17 at half-time and, after a penalty from the hosts, moved into a 31-20 lead, before Tynedale hit back to grab the win.
Worthing sit 11th in the table and host fifth-placed Esher on Saturday (October 19).