Dominic Shepherd netted the only goal of the match after just eight minutes from a Charlie Romain cross to set up a clash in the last eight against County League leaders and holders East Preston at The Lashmar.
Pagham felt they were denied a penalty on 17 minutes as James Temple went down under pressure, but nothing was given, while the hosts’ best chance came five minutes before the break when Joe Booker headed over from close range.
After the break, both sides had chances as Lancing goalkeeper James Shaw was called into action, while, at the other end, Owen Callaghan forced just as good a save out of Pagham’s James Binfield.
Lancers’ Jonno Melia had a fine shot on 77 minutes saved again by Binfield, while a superb strike on the left by Ryan Cox was only just rescued by Shaw.
Lancing manager Richard Whittington said: “It was a really good win and a great team performance. We defended really well and, athough we didn’t have too many chances, we took one early on and ground it out.
“We have more of a settled side now and we knew it would take a while to get going, but after a couple of months we have settled and are pretty much there now, although not the finished article.”