Responding to a total of 232 for nine, the visitors romped home with 4.1 overs to spare to inflict the heaviest defeat suffered by Essex in a limited overs match.
The previous record was also against Yorkshire, by nine wickets at Headingley in 1982.
Gale, in recording his first century in limited overs, finished with 125 that came off 115 balls and included 12 fours and three sixes.
Rudolph contributed 101 from 102 balls with the help of 13 boundaries.
Their partnership represented their highest for any wicket in one-day league cricket.
The nearest Essex came to breaking it was when the total had reached 64. Gale, 30 at the time, thrashed hard to cover point where Tim Phillips put down a difficult chance low down.
But from then onwards, the Yorkshire pair progressed with embarrassing ease while plundering runs from seven bowlers.
Yorkshire's other star was West Indies paceman Tino Best who picked up 4-46 in his eight overs.
It all left Grant Flower probably wondering what he needs to do to finish on a winning side.
In recording his first limited-overs century in English domestic cricket, the Zimbabwean showed he is still a force to be reckoned with even though he is in his 40th year.
He arrived after the first two wickets had gone down in the opening four overs and skilfully found the gaps against both pace and spin to keep the scoreboard ticking over.
Flower's innings was punctuated with seven fours and a six, this at the expense of spinner David Wainwright when he launched him over long off, and the only other batsman to put together a worthwhile contribution was skipper Mark Pettini.
While Flower ended with 113 not out from as many deliveries, Pettini struck 51 from 56 balls, before cutting Wainwright to backward point.
That dismissal brought to an end a partnership of 81 in 15 overs and none of the remaining batsmen got beyond 16 as Best made his presence felt.
He destroyed the middle order after earlier bowling England opener Alastair Cook with a full toss in his first over.
Cook's only scoring stroke was a lofted drive to the boundary from a free hit that followed a no ball.
It all added up to a fine start for Yorkshire who came into this game having won their opening two matches in the LV= County Championship.
For the full report and reaction read Sports Monday inside tomorrow's Yorkshire Post.