The Diamond Eagles ended Sussex's Champions League campaign by defeating the Sharks in a 'Super Over' after scores were tied at the end of the regulation 20 in Delhi.
Sussex managed only 7-119, Joe Gatting top-scoring with 25 and Ed Joyce contributing 21.
Opener Rilee Rossouw hit 65 off 62 balls as the Eagles appeared set to reach their target easily.
But Sharks spinners Piyush Chawla and Rory Hamilton-Brown pulled things back, and the South Africans managed only to tie scores – 4-119.
The 'Super Over' rule - an extra over with teams permitted only three batsmen and one bowler and the 'innings' ending if a side loses two wickets - was applied.
The Eagles managed 10, while Sussex lost two wickets off the first two deliveries to hand its opponents victory and a berth in the second round.
Luke Wright had given Sussex some momentum with the bat at the start of the match.
But after clubbing Cornelius de Villiers for a six and four, he lost his off-stump attempting another big hit to leg.
Chris Nash followed his opening partner back, the first of Dillon du Preez's two victims - and de Villiers pulled off a spectacular caught and bowled to send back Hamilton-Brown.
Joyce and captain Michael Yardy - back after missing his team's first match against New South Wales Blues because of an illness - briefly held the innings together.
But it was the stand between Joyce and Gatting which carried Sussex past the 100-run mark.
Gatting, by far the most fluent of Sussex's batsmen, dominated a 29-run stand for the sixth wicket.
Rossouw's response on a low and slow surface contained some powerful hitting down the ground, as the Eagles' chase began well.
He smacked five boundaries and two towering sixes inside the first six overs and brought up his half-century in just 39 deliveries.
The left-hander's opening partner Adrian McLaren contributed only 16 in an opening stand worth 72.
Rossouw was dropped on 26 by James Kirtley at short fine-leg; wicketkeeper Andy Hodd missed a chance offered by McLaren on 10.
Chawla, who eventually accounted for McLaren, missed an obvious chance to run out Rossouw at the non-striker's end just after the batsman had reached his 50.
The Eagles were on course. But Chawla applied the brakes with his leg-breaks.
Off-spinner Hamilton-Brown then bowled Boeta Dippenaar and dismissed Rossouw too in the penultimate over.
The Eagles needed 12 off the last over, and Pakistan seamer Yasir Arafat conceded three singles first up.
But Ryan McLaren managed an inside-edged boundary off the fourth and then struck another four over midwicket to tie the scores.
Arafat was nominated for the 'Super Over' and conceded nine runs, for the wicket of Rossouw - who was run out.
For the Eagles, De Villiers bowled Dwayne Smith and Hamilton Brown with his first two deliveries.