United made four changes to the side that defeated Little Common in midweek, with Patryk Miszkiewcz, Linton Rogers and Ashley Darby coming into the starting XI, alongside debutant Joe White who started at left back.
The first half was almost all United, as Storrington sat deep inside their own half with 10 men behind the ball as they looked to soak up United's attacking threat.
Wes Tate was inches away from giving United the lead as his drilled cross evaded a host of outstretched legs and narrowly flew the wrong side of the post.
Soon after, Rogers made space on the right wing to tee up Matt MacLean, but his header was tipped over the bar by Storrington 'keeper Elliott.
Rogers again found space behind the home defence as he broke away down the left wing and rolled the ball across to Jack Divall who slotted past Elliott to give United the lead.
The second half saw Storrington begin to venture forward with a more attacking setup, but United rarely looked troubled.
Rogers almost doubled the United lead midway into the second half as his scissor kick grazed the crossbar.
Rogers was unlucky not to be awarded a penalty soon after when he appeared to be scythed down from behind by Iain Jarvie, but the match official saw the incident in a different light and waved play on.
Grant Young was called into action for the first time on 78 minutes and produced a fine save with his feet to deny Harry Jarrett.
With less than ten minutes left, the victory was secured as Ben Dartnall scored his first ever goal in United colours after a left footed effort from 20 yards that left the 'keeper stranded as Dartnall wheeled away to celebrate in front of the visiting United fans with his unique version of a salmon dive.