The kick-off gave an indication of how the first half would pan out as Mark Pulling immediately gave the ball to the impressive Joel Bingham, who fed former Worthing frontman Gavin Gordon, but the Mussels were saved by the legs of James Shaw in the first minute.
The visitors did open the scoring after eight minutes, however, as the lively Chris Gregson raced onto a Bingham through ball to slot home past the advancing Shaw.
Gregson would have had a second on 22 minutes had it not been for a last ditch Dan Jordan challenge as he was about to pull the trigger.
Redhill did double their lead after 25 minutes, and it was Gregson once again, heading home a Bingham flick from a corner from just four yards out with his marker nowhere to be seen.
The half finished with the visitors two goals to the good but only due to the efforts of Shaw, who repeatedly frustrated Gregson’s quest for a hat-trick.
Shoreham were clearly given some home-truths at half-time by joint manager Mark Burt and started the second period far brighter but failed to create any meaningful chances. Only Gareth Green’s thunderous volley from 20 yards troubled the Redhill goal.
Mussels went three goals behind in the 71st minute as Gordon caught them on the break with a long-range lob, having collected Gregson’s flick, arguably the most difficult of the numerous chances he had been offered during the game.
Redhill wrapped up the game with another lob, this time after substitute Lee Radford had cut in from the left wing on 79 minutes.
It could have been worse for Mussels had Jon Difford’s perfectly-measured free kick from the halfway line not been disallowed, owing to the ball apparently rolling, with four minutes to go.
Owen Callaghan could have grabbed a consolation in the final minute from Josh Clayman’s cutback, but the winger put his shot just the wrong side of the post.
Burt said: “We were beaten by a good side but we gave the ball away far too much during the first half. We got better in the second half, so I was pleased with that but they just hit us on the break.”