After Darren Annis headed home Jamie Groves' cross to give Mussels an early lead, Wick fought back with two goals inside three minutes midway through the first half.
Firstly, Julian Boniface headed home on 19 minutes and then Steve Davies fired home.
Phil Turner extended the lead three minutes into the second half, before Colin Moss headed in Daren Pearce's corner to make it 4-1 on 62 minutes.
Shoreham got a goal back through Dean Smith on 83 minutes, but Wick comfortably held on.
East Preston moved four points clear of the relegation zone in Division 1 with a 3-0 victory over Lingfield. Lee Farrell netted a brace and Terry Dodd was also on target for EP.
Worthing United played their first game for more than a month but went down 1-0 at home to Three Bridges.
Arundel's match at Hailsham was postponed owing to a waterlogged pitch.
In Division 2, Mile Oak stayed top with a 2-0 win over Storrington courtesy of goals from Lloyd Skinner and Chris Paine.
Third-placed Rustington went down to a 3-1 defeat at Sidley. Steve Kirkham struck for Blues.
Southwick moved back into fifth place with a 4-2 win over Westfield. Player-manager Dominic Shepherd scored twice, and an own goal and Adam Steele were their other scorers.
Lancing recorded a 3-2 success at Bexhill with goals from Ryan Loversidge, Scott Hunt and Rob O'Toole.
Littlehampton lost 2-1 at home to Wealden, with Jerry Manning scoring for Golds in the last minute.
Steyning Town's home match with Rye was postponed owing to a waterlogged pitch.
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