Worthing lost 29-27 after the visitors’ Gary Kingdom kicked over a drop goal in the final play of the game.
Raiders had led 24-9 at half-time, before Taunton fought back in the second half.
Raiders fell behind to a drop goal from Toby East on five minutes but responded with their first try of the afternoon just four minutes later.
Jamie Redmayne brilliantly offloaded the ball to Alex Nielsen, who burst through to touch down and Matt McLean converted.
A penalty from Taunton’s Kingdom reduced the gap to a point on 13 minutes.
Raiders increased their lead just two minutes later when they superby drove forward from a line-out and Rob Smith touched down, with McLean again converting.
Kingdom nailed another penalty five minutes later to make the score 14-9, before McLean put a penalty over on 29 minutes.
Raiders added their third try on 35 minutes when Calum Waters fed Kieran Leeming, who quickly offloaded the ball to Simon Gaynor, and he went over. McLean’s conversion made the score 24-9, before Worthing had to stand firm under intense pressure as the half drew to a close.
Taunton started the second half strongly and Raiders had Gaynor sinbinned on 46 minutes.
Raiders’ Liam Perkins and Dan Sargent were held up on 50 minutes, before Leeming looked to kick the ball over the visitors’ defence. His kick was charged down by Kingdom, though, and the Taunton man raced the length of the pitch to touch down and he then converted to make the score 24-16.
Taunton closed the gap to just a point with a converted try from Paul Davis on 59 minutes, before they took the lead with a Kingdom penalty on 68 minutes.
Raiders responded immediately with a penalty of their own from McLean to take a 27-26 lead a minute later.
Kingdom kicked a penalty wide on 74 minutes and then saw a drop goal attempt hit a post on 79 minutes, before he kicked over the winning points with the final action of the game.