Kaif made 55 from 62 balls with four boundaries as Derbyshire raced to 163 in 30.5 overs in the second division match with seven balls to spare, overhauling the 160-run target set by Sussex in the rain-affected match on Sunday.
The Indian youngster combined well with Dominic Hewson, who made a 29-ball 39, for the fourth wicket to take the score from 65 for three to 129 when Hewson departed 32 runs short of the victory.
Earlier, Sussex were helped by a 55-ball 60 from Matthew Prior, but some good bowling from Graeme Welch (2/27) and Dominic Cork (2/34) restricted them in the 45-over match which was shortened to 32 overs due to rain.