The third-placed Bears were bowled out for 182 in the final over replying to Sussex's modest total of 199 for nine, and Sussex now need to beat Yorkshire and Kent to secure their place in the last four. However, Warwickshire and Kent can still go through if the leaders slip up.
Sussex's spinners were the key to this victory. They bowled 21 overs between them on a slow pitch with Michael Yardy setting the tone by conceding just 23 runs in his eight overs of left-arm spin at the start of the reply, before leg spinner Will Beer took centre stage.
His throw ran out Will Porterfield and, when he came into the attack, Beer had Tim Ambrose (21) caught behind off a thin edge before drawing Jim Troughton forward and enabling wicketkeeper Ben Brown to stump the Bears' skipper for 30. Beer then bowled Darren Maddy off an inside edge on his way to figures of three for 27.
Off-spinner Chris Nash had the dangerous Rikki Clarke caught at extra cover and he returned to the attack in the 38th over to end a threatening seventh-wicket stand of 52 from 45 balls between Keith Barker and Stefan Piolet by bowling the former as he tried to clear the leg side boundary.
That left Warwickshire needing 34 off the last three overs and Nash secured victory in the final over when he bowled Chris Wright to finish with 3 for 27.
Earlier, Sussex had been indebted to Yardy who made the only half-century of the game and was the only batsman on either side to prosper on a slow pitch.
Chris Wright took three wickets in nine balls - including Luke Wright for a golden duck - to reduce Sussex to 34 for three in the seventh over, but Yardy and Murray Goodwin put on 62 in 12 overs before Goodwin played on to Jeetan Patel's quicker ball for 36.
The New Zealand off-spinner also picked up Joe Gatting to finish with two for 29 and at 125 for six in the 27th over Sussex were in trouble but Kirk Wernars counter-attacked in a stand of 54 in nine overs before Yardy chipped a catch to mid-on, having hit five fours in his 61.
Wernars finished with an unbeaten 37 off 34 balls and a target of 200 proved beyond a Warwickshire side whose hopes of reaching the last four may have been fatally damaged by two defeats in the space of 48 hours.
Yorkshire had the edge in their County Championship clash with promotion rivals Derbyshire at Headingley before rain ended play for the day just one delivery after the lunch interval.
Put in to bat, Yorkshire had scored at over a run-a-minute to finish on 127 for two with opener Adam Lyth unbeaten on 60.
They had started the day in joint second place with Hampshire and need every point they can muster if they are to gain promotion ahead of the club's 150th anniversary next year.
Elsewhere, a century by Stewart Walters helped Glamorgan to 242 for three and put them in control of their match against Essex at Colchester.
The 29 year-old Australian struck an unbeaten 129 and rarely played a false stroke against an Essex attack that sorely missed its spearhead David Masters.
Rob Newton reached the close unbeaten on 46 while Stephen Peters earlier made 47 as Northampton reached the close of a rain-affected day at the Rose Bowl on 170 for five against Hampshire.
Rob Newton and James Middlebrook dug Northamptonshire out of potential trouble at the Ageas Bowl with an unbroken stand of 72 after hosts Hampshire had threatened to get on top.
Only 48 overs were possible because of morning rain, with the visitors reaching 170 for five after Hampshire captain Jimmy Adams decided to field first on a green wicket which helped his seamers early on.
No play was possible on the opening day of the match between Gloucestershire and Kent at Bristol.