The visitors proved too strong in the second half and turned around a 21-10 half-time deficit to take a deserved 36-28 victory.
Raiders, who were looking to climb out of the relegation places with a victory, had to settle for just a bonus point in their battle to avoid an immediate return to National 2 South.
Jordan Burns touched down two tries and Ollie Richards and James Chisholm also scored for Raiders, while Joe Govett enjoyed a successful day with the boot.
But Worthing succumbed to Richmond’s frustrating kick and drive game in the second half, which provided a poor spectacle for the healthy crowd.
In terms of other results, it could have been worse for the home side, with Henley Hawks and Cinderford both losing.