James Kirtley and Mark Robinson scrambled a bye off the final ball as Sussex tied with Leicestershire.
Chasing 165 on a bowler-friendly pitch, Sussex appeared to have blown their chance when five wickets tumbled in five overs the day after they had lost six wickets for ten runs at Gloucestershire.
Ten runs were needed off the last over and Umer Rashid gave the county hope by scoring seven of them before he played on to Chris Lewis off the penultimate ball. Robinson, who had earlier equalled his career best limited overs bowling performance, missed the final ball but wicket keeper Neil Burn's wayward throw allowed Kirtley to make his ground.
Two points are better than none, but this was another game that Sussex threw away. Michael Bevan and Richard Montgomerie, who returned to form with a patient 42, put on 66 in 19 overs for the third wicket before Montgomorie chased a wide one from Lewis and was caught behind.
Sussex needed 50 off 10 overs at that stage and were still on course, but alarm bells started ringing when Bevan was dismissed for the first time in one day matches this season after making 59 from 83 balls.
Tony Cottey and Robin Martin-Jenkins were both run out as the asking rate crept up, Jamie Carpenter was caught trying to hit over the top and Nick Wilton played on to Lewis off the second ball of the final over.
Earlier Robinson spearheaded a professional bowling effort by Sussex, equalling his previous best figures in one day cricket with 4-23. Martin-Jenkins made the initial inroads with wickets in successive overs before Robinson worked his way through the middle order.
Darren Stevens, who took a championship century off Sussex's attack at Arundel last year added 41 in nine overs with Darren Maddy before he became Robinson's first victim. Aftab Habib's undefeated 39 helped Leicestershire post a competitive total.
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