Joe Keehan gave Mussels the lead from Scott Packer’s cut-back inside a minute.
Lancers thought they should have had a penalty when Mike Williamson went down, before Shoreham scored twice in three minutes to go 3-0 ahead.
Tom Burton headed home Jamie Cradock’s cross on 38 minutes, before Keehan scrambled the ball home after Andy Pearson knocked Packer’s free kick back across goal two minutes later.
Alex Fair got a goal back late in the first half but Mussels comfortably held on to all three points.
Shoreham boss Bryan O’Toole said: “We were pretty comfortable in the first half but it was difficult in the second half as the pitch was so heavy. The boys did well, though, and now we just need 14 more wins. How we play will go out of the window soon as you just have to find a way to win games.”
Lancing manager John Sharman said: “We got off to a very disappointing start but I thought we should have had a penalty for a foul on Mike.
“We didn’t create that many chances in the second half but gave a good account of ourselves against a top side, so it’s onwards and upwards.”
Shoreham are at Little-hampton on Monday, while Lancing host Worthing United. Both games kick off at 11am.
SHOREHAM: Heyburn; Hartley, Storrie, K.Keehan, Pearson, O’Hagan, Packer, J.Keehan, Deen, Burton, Cradock. Subs: Greenfield (Cradock 60), Gould (Packer 65), R.O’Toole (Burton 80).
LANCING: D’Cruz; Kavanagh, Berry, D.Sharman, Fenton; Baah, Caplin, E.Finney, Williamson; L.Finney, Fair. Subs: Costen (Kavanagh 70), Bennett (Baah 75), Frankling (Caplin 82), Heath, Green.
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