Storey welcomed back Max Thompson and Alfie Peacock after both had been absent through illness.
United took the game to the visitors, looking to get an early lead, and the breakthrough came 10 minutes in when a brilliant move down the left led to Tigana Quebe crossing for Thompson to finish at the near post.
EP found themselves 2-0 down 15 minutes later. A shot from Quebe flew through a crowd of players into the far corner.
Just before the half, United could have gone 3-0 up but for a brilliant save from a close-range shot that the visitors’ goalkeeper deflected over the crossbar.
The second half saw United coming out with hunger to increase their lead, not letting the opposition come out of their own half in spells.
Chances were still being created but the EP keeper stood firm.
This was another first-rate performance by Storey’s side that completed an unbeaten October.
Also celebrating three SCFL premier points at the weekend were Eastbourne Town, who triumphed 2-0 at Crawley Down Gatwick thanks to second half goals from Jack Samways and Leon Greig.
Tuesday evening saw United and Town record a pair of wins.
United came from behind to claim a 3-2 victory at ten-man Pagham in the SCFL premier.
The visitors led 1-0 at the break thanks to Thompson’s second minute strike. Early second half goals from Pagham’s Joe Clarke and Ryan Morey turned the game on its head. But an own goal and a second for Thompson saw United take the points.
Town advanced to the third round of the RUR Cup thanks to a 2-0 win at Hailsham Town. Leke Ademola and Louis Veneti struck late on for Town.
Tomorrow Eastbourne United go to Varndeanians again, this time in the league, while Eastbourne Town host Steyning.
Meanwhile in the Sussex Senior Cup, United will be away to Mile Oak while Town will face Shoreham.
Eastbourne Borough will make the trip to Roffey.