Golds have been reinstated into the competition - and will host Brockenhurst in the fifth round on Saturday, February 12 - after the London side were thrown out for fielding an ineligible player in their win over Town.
The fifth round is the last 16 of the Vase and winning clubs will pick up £2250 from the competition prize fund and the losing clubs £725. A win would leave Golds just two more wins from the Wembley final.
Newham beat Littlehampton 5-0 in round four with joint boss Mitchell Hand admitting afterwards they'd been beaten by the better team.
It is believed Newham have only until tomorrow to appeal against their expulsion.
A statement on the Littlehampton Town website said: "Littlehampton Town Football Club have today received confirmation from the FA that we have been reinstated into the Buildbase FA Vase (subject to appeal) and we will now take our place in the Fifth Round of the competition.
"This is following Athletic Newham fielding an ineligible player under the competition specific sanctioning rules in the Fourth Round. We will welcome Brockenhurst to The Sportsfield for a 3pm kick-off.
"This now means our away match in the league against Crawley Down Gatwick, originally on the 12th February, will now be rescheduled for another date. More details, including admission prices, will follow in due course."
The Vase reprieve comes in what's already a remarkable season for Hand and George Gaskin's team - they lead the Southern Combination premier division after promotion last year, having scored 94 goals in their 25 league games so far. They beat Broadbridge Heath 2-1 last week then drew 2-2 with Pagham on Tuesday night.