Yorkshire set Sussex a victory target of 201 in the Clydesdale Bank 40 at Headingley.
In a rain-affected match reduced to 28 overs a side, the Tykes posted 200-8 after losing the toss and being invited to bat.
Captain Andrew Gale top-scored with a quick-fire 43, while Joe Root made 41 before being brilliantly caught and bowled by Chris Nash.
Tim Bresnan added 27 useful runs down the order to help Yorkshire post what looked a decent total, with Sussex needing to score at 7.14 per over to win.
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