Nottinghamshire missed the chance to seal their place in the semi-finals of the Yorkshire Bank 40 after Sussex reached a daunting target of 291 to win by four wickets at Hove.
Sussex were led to victory by skipper Ed Joyce who carried his bat for an unbeaten 123, the 13th one-day hundred of his career.
Opener Alex Hales made 101 and David Hussey 82 as Nottinghamshire plundered 105 off the last 10 overs to post a formidable total of 290-5.
But Luke Wright and Joyce launched the reply with 112 off 13 overs and even when Wright fell for 62, Matt Machan, whose 51 came off just 28 balls, maintained the momentum.
Sussex wobbled briefly towards the end of their chase before they got home with nine balls to spare.
Nottinghamshire now need to beat Kent at Canterbury in their final game on August 26 to make sure of their place in the last four. If they lose Northamptonshire, who are a point behind them in Group C, will go through instead if they win their last match against Warwickshire in Birmingham.
The Outlaws made a bad start after winning the toss and batting first. Michael Lumb was lbw to the third ball of the innings from Lewis Hatchett and the same bowler picked up a second wicket in the third over.
James Taylor, who played for Sussex last month as a guest against Australia, was superbly caught low down by Chris Jordan at slip to leave the Outlaws 11-2.
But that was Sussex's last success for 16 overs as Hales and Samit Patel rebuilt the innings with a stand of 102 before Chris Liddle had Patel caught on the long-leg boundary off a slog-sweep for 43.
Hales reached his 50 off 43 balls with his sixth boundary and went to his fourth List A hundred off a further 44 deliveries with 11 fours and a pulled six off Jordan. Two balls after reaching three figures he was superbly caught by Rory Hamilton-Brown running in from the long on boundary.
Hussey had been dropped on 17 at short cover by Mike Yardy and he made the most of the reprieve, adding 81 in 45 balls with Riki Wessels (34) as he finished undefeated on 82 from 64 balls with seven fours and a six.
A score of 290 should have been defended but the Outlaws bowled poorly from the start and Sussex had 71 on the board at the end of the eight-over power play.
Wright, who made 114 on Tuesday against the Netherlands, was soon into his stride as he reached 50 from 33 balls and it was a surprise when he fell in the 13th over to a catch on the mid-wicket boundary after making 62 from 49 balls with three sixes and four fours.
He had given Sussex the perfect platform and Machan was soon taking the Outlaws' attack apart, reaching his half-century from just 25 balls. He was caught at short fine-leg off Hussey for 51 but Sussex needed 83 from 17 overs at that stage and Joyce was in no mood to let the advantage slip.
There was a brief wobble when the Sharks lost four wickets for 26 in seven overs and things might have been different had Patel not spilled a straightforward chance at extra cover when Joyce was on 108.
But Will Beer joined him to contribute an unbeaten 20 and sealed victory with a six off Jake Ball. Joyce's 123 - his second one-day hundred of the season - came off 109 balls with 16 boundaries.