Victory moved Sussex up into sixth spot - 18 points ahead of second from bottom Hampshire who do have a match in hand.
It was their first win in nine games since defeating Warwickshire by one wicket at Hove in late May and their fourth in total this season.
But in contrast Worcestershire have slipped to the bottom of the table, 13 points adrift of safety and they have played a game more than seventh-placed Somerset.
The bottom two go down and Sussex can virtually assure themselves of safety with a home win ovser Somerset in match starting on Monday week.
Only a superb 100 by 19-year-old Joe Clarke - his first in the competition - delayed the outcome.
The home side were outplayed in all departments and never recovered from being bowled out for a below par 210 in their first innings after winning the toss.
They will have to double their win tally for the season by triumphing in their final two matches away to Durham and at home to Middlesex to have a realistic chance of survival in the top flight for a second successive season.
It was not the way spinner Saeed Ajmal would have wanted to sign off at the completion of his third spell with Worcestershire.
He has been less effective in red ball cricket this summer with his remodelled action and collected only 16 wickets from eight matches at an average over 50.
England players past and present were chiefly responsible for Sussex’s win with Luke Wright hitting a career best 226 not out and fit again Chris Jordan finishing with seven wickets in the game.
Worcestershire resumed on 59-3 and Jordan, their first innings destroyer with 5-68 off 22 overs, quickly broke through when bowling nightwatchman Charlie Morris for 12.
There was then a rain delay which led to the loss of 12 overs.
But Sussex spinner Ashar Zaidi quickly made up for lost time by trapping Alex Gidman lbw for six to leave Worcestershire on 83-5.
Then in the last over before lunch Jordan struck again as Ross Whiteley went lbw for two.
More prolonged resistance came during the afternoon session as keeper Ben Cox proved an effective ally to Clarke.
Clarke went to a classy half century off 90 balls with eight boundaries.
It was Sussex seamer Ollie Robinson, after reverting to spin mode, who broke the stand when Cox (31) went for a slog sweep and was bowled.
Zaidi claimed his third wicket of the innings as Joe Leach (7) became the fourth lbw victim of the innings.
Sussex moved within one wicket of victory when Jack Shantry (13) was also given out lbw but Clarke had time to reach three figures off 174 balls with his 14th four - at Jordan’s expense through the covers.
It all ended when Steve Magoffin bowled Ajmal (9) to leave Clarke unbeaten on 104 out of 237 all out.
Sussex vice-captain Chris Nash, who captained the side in the absence of the injured Ed Joyce, said: “That is a huge win for us against a team close to us in the table. There is now a bit of a gap and it is a nice position to be in having things in our own hands.
“It was a flat pitch but we worked hard for four days and everything we set out to do, we achieved basically.
“If you look at the game, Chris Jordan bowled a world class spell on the first day on a flat pitch and that set things up nicelty for us for the remainder of the game.”
Worcestershire centurion Clarke had mixed feelings.
He said: “It’s great to get my maiden first class hundred but on the flipside to get it in a losing cause isn’t as sweet really.
“I’ve come close a few times, an 80 and a 70 and all of the lads have been saying ‘when is it going to come.’
“Getting a one-day century was a massive help, making me realise I could get to a hundred.”
On the defeat, Clarke said: “They bowled in better areas than us, had better plans and getting 210 in the first innings was nowhere near good enough on a good wicket first day.
“They’ve cashed in, got a good score and once you are behind in the game like that, it is hard to come back.”
Don’t miss out on all the latest breaking sports news where you live.
Here are four ways you can be sure you’ll be among the first to know what’s going on.
1 Make this website your homepage
2 Like our Facebook page at facebook.com/pages/Sport-Sussex
3 Follow us on Twitter @SportSussex
4 Register with us by clicking on ‘sign in’ (top right corner). You can then receive our daily newsletter AND add your point of view to stories that you read here.
And do share with your family and friends - so they don’t miss out!