Yorkshire rattled up 302 for four in front of a 6,500 crowd, before bowling out their opponents for 267, although they are too far down the table to stand any chance of reaching the semi-finals.
Rudolph, who hit 120 in the Championship clash between the sides on Saturday, was again in tremendous form after Yorkshire had been put in to bat.
The South African left-hander opened the innings and led the charge with an unbeaten 132 off just 112 deliveries with 11 fours and three sixes.
It was Yorkshire’s fifth highest individual knock in this form of cricket and Rudolph’s seventh century in the competition as well as his seventh three-figure score in all matches at North Marine Road.
Rudolph was not the only star of the show, however, because Adam Lyth contributed a sparkling 73 off 68 balls with eight fours and a six in an opening stand of 142 in 22 overs.
Jonny Bairstow, who will now join up with England’s one-day team for their one-off game in Dublin this week, also hammered 52 from 45 deliveries with two fours and three sixes while helping to put on 113 for the second wicket in 14 overs.
Ed Joyce made the right sort of start for Sussex with three consecutive boundaries off Oliver Hannon-Dalby who was immediately replaced by leg-spinner, Adil Rashid.
He was also hit for two fours by Joyce who then drove hard to mid-off where Hannon-Dalby held on to a splendid catch.
Yorkshire tightened their grip as Steve Patterson struck twice, Nash flicking straight to Bairstow on the mid-wicket boundary and Murray Goodwin driving to Rashid at cover.
Brown received 41 balls for his half-century with three fours but Yorkshire were back in charge now and after Moin Ashraf deservedly got a wicket by bowling Liddle the match ended with the running out of Brown in the 37th over.
For the full report and reaction to the weekend’s cricket read Sports Monday inside tomorrow’s Yorkshire Post.