After being beaten in their first-ever match at this level by South Park on Saturday, efforts from Scott Kirkwood, Toby House and a stunner from substitute Darren Boswell sealed a 3-0 success for Horsham at Culver Road.
Hornets, who are playing all home matches at Sussex FA HQ this season while work on their new stadium is undertaken, had too much quality for Sammy Donnelly's side.
Shoreham served up a decent defensive display in the opening half-hour, before falling behind to a Kirkwood spot-kick.
Mussels looked light on ideas from then on, with second half efforts from House and a Boswell stunner earning Hornets a first league win of the season.
Mussels had the first opening of the match, going close inside three minutes. Mitchell Hand's clever slide pass down the side of Chris Breach sent Archibald clear but Michael Hunter in Hornets' goal was equal to his angled drive.
Despite seeing the vast majority of the ball, Horsham were struggling to create any clear openings.
Daniel Simmonds headed down into Ross Myers' path on 17 minutes, whose fizzed, looping shot went just wide of the far post as Sammy Donnelly's went near once more.
Shoreham goalkeeper James Broadbent was first called into action six minutes later. Darren Budd's corner was cleverly flicked towards goal from the head of Rob O'Toole but Broadbent was equal to his effort.
Horsham were then gifted the chance to go ahead on the half-hour, having looked short on ideas. Mussels debutant Ryan Woodford went through Toby House in the area with referee Steven Hughes pointing to the spot. Scott Kirkwood sent Broadbent the wrong way with his penalty as Horham went in front.
Kirkwood should then have doubled his and Hornets' tally five minutes prior to the interval. O'Toole's superb reverse path played Kirkwood in behind but Broadbent stopped his strike.
Hornets were quick out of the blocks in the second, with O'Toole's fierce drive going just over the bar seven minutes after the restart.
Midfield man Darren Budd drove forward less than a minute later, before sending a long-range strike inches wide of the far post.
Horsham's pressure paid off with a second goal on the hour. O'Toole's cross picked out an unmarked House to fire home from all of six yards.
The home side then had things wrapped up courtesy of a super strike from substitute Darren Boswell. The winger was allowed time on the ball, before thundering a 30-yard strike into the top corner.
Mussels kept pushing right until the end and Simmonds fizzed a strike just wide of the far post ten minutes from the end. However, Hornets kept their clean sheet intact and claim their first three points of the campaign.
SHOREHAM: Broadbent; Packer, Denyer, Watson, Gathern, Hand; Woodford, Myers, Burton; Simmonds, Archibald. Subs: Caplin (Myers, 78), Goldson (Woodford, 85), Nayee, Quadri (Archibald,82)
HORSHAM: Hunter; Hunt, Breach, Hyde, Duncan; Keehan, Budd; House, Kirkwood, Nicholson; O'Toole. Subs: Lawley, Boswell (Nicholson, 35), Farmer (Duncan, 35), Thurgar (Kirkwood, 69), Axell.