Swans keeper Gary Elliott kept his side in the game with a string of saves before Storrington thought they had gone ahead but the offside flag denied Kristian Harding.
Clymping set the tone early on when Billy Rayner's long-range drive was well saved by the excellent Gary Elliott and the Storrington keeper was called upon again shortly afterwards when he denied Tony Castro.
In truth, Swans were fortunate to still be in the game as a whole host of chances continued to fall Clymping's way. Joe Shelley shot wide, Rayner had a header saved and Richard Ghent went close before Storrington thought they had gone ahead against the run of play when Kristian Harding tucked away Craig Grantham's cross-shot, only to see the flag raised for offside.
That would have been harsh on Clymping, who went ahead in the 40th minute. Richy Moss' inswinging corner fell to Seb Di Paola, who headed in for his third goal in as many games.
The second half continued in a similar manner with Clymping creating the chances. Moss' accurate cross from the right just evaded Ghent at the back post and Paul Young fired just over.
Harding blazed over when well-placed to compound Swans' woes and Clymping wrapped the game up right on full-time when Dave Gaskin played in Shelley, who clinically fired home from 10 yards.
Storrington midfielder Stuart McCall said: "It didn't happen for us and it's been a very frustrating season. We've had ups and downs and there's no consistency whatsoever. No one's sure why but it's very strange."
Swans manager Ricky Hamilton was bitterly disappointed with his side after their 3-2 defeat at home to Wealden on Saturday.
Swans trailed 3-0 inside 23 minutes and Hamilton said: "The opening half hour was the worst I've ever been associated with.
"We got back in it, though, and could have got something '“ but that would have papered over our problems.
"I can't even call our defending schoolboy as that would have been detrimental to schoolboys.
"It wasn't good enough for the club and wasn't good enough for me. It's not acceptable and it's my job to make sure it doesn't happen again. I made a couple of changes at 3-0 down but if I'd had eight substitutes and was allowed to use them all, I would have done.
"We've under-achieved this season with the quality we have in the squad. I was looking at the top six, which I think is now beyond us, so we've got to make sure we finish in the top half, as that will show progress from last season."
Two Harding goals, both from Steve Tasker crosses, were the only positives for Hamilton as Swans got the score back to 3-2 at half-time.
They went close to equalising but James Davis' shot hit the bar and Liam Humphreys and Tasker also went close.
STORRINGTON v Clymping: Elliott; Davis, Potter, Watton, Sleat; Ayres, Rhodie, McCall, Humphreys; Harding, Grantham. Subs: Blaydon (Watton 45), Bradshaw (Ayres 80), Carter (Sleat 83).
v Wealden: Elliott; Davis, Blaydon, Carter, McCall; Tasker, Rhodie, Humphreys, Tidman; Harding, Grantham. Subs: Humphreys (Carter 25), Sleat (Tidman 35), Potter (Grantham), Beaumont.
Worthing United edged to within four points of Division 2 leaders Loxwood on Saturday after they ground out a tight 1-0 win from a tough trip to Westfield.
United joint manager Jason Rutherford said: "It was a great win, if you want to go up, as we do, you need to win at places like Westfield.
"We didn't let them play and our three-man midfield was effective in stopping them. Results went our way and we played at a high tempo.
"Enzo Benn has been a great signing for us and we've improved since he's joined us."
Paul Elliott netted the only goal, a 25-yarder into the top corner, on 31 minutes.
WORTHING UNITED: Standen; Hunt, Curnow, J.Elliot, Philpott; Benn, Hibberd, Joseph; P.Elliott, Annis, Green. Subs: Bentley (Annis 80), Herbert (P.Elliot 82), Moody.
Lancing returned to winning ways in Division 2 with an impressive 3-0 win over leaders Loxwood, and manager Martin Gander was delighted with his team's performance.
He said: "It was a great performance and we showed what we're capable of. Keeping the clean sheet was most satisfying of all as we've not had enough of them. The attitude we showed and the tempo we played at was superb."
Lancers went in at half-time one up after a flowing move involving Michael Sims and Darren Boswell resulted in Lee Garnham firing home in the 20th minute.
The second half continued in a similar manner and Lancers doubled their advantage five minutes after the break, when Darren Boswell pulled the ball back for Danny Clayton to convert.
Dan Griffin scored the third four minutes from time from another Boswell cross to complete an emphatic victory.
LANCING: Green; Ford, Early, Mighall, Proto; Beard, Sims, Garnham, Boswell; Clayton, Griffin. Subs: Burton (Clayton 75), Coughlin, Skipper (Sims, Garnham 82), Gander, Goacher.
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