In barely visible conditions due to thick mist and fog, Leeds survived a scare in the opening minutes as a cross from the right picked out Lewis Koumas whose shot from point blank range was saved by Illan Meslier.
After a frantic opening, Leeds eventually settled and created a host of chances but without any finish, Manor Solomon missing an open goal when volleying wide on the stretch to a Dan James cross.
The first half looked set to end goalless but Leeds went ahead in the 43rd minute after a precise rising finish from Joel Piroe who was played in by Brenden Aaronson and eventually netted after Viktor Johnasson spilled his attempts to smother at his feet.
Stoke again began the second half with a bit of intent but Leeds were soon back dominating and Piroe bagged his and United's second in the 63rd minute, heading into an empty net from a neat looping James cross.
Leeds then squandered a host of chances to add to their tally but the three points were well and truly in the bag against a poor Potters side. Leeds United writer Joe Donnohue hands out the ratings from a Boxing Day night to savour for Whites fans in the Potteries.
1. Illan Meslier
8 - Made an important stop inside the opening two minutes from Lewis Koumas that would have given Leeds a horrible evening had it gone in. No handling mishaps or footwork errors despite tricky, foggy conditions. Photo: Ben Roberts Photo
2. Sam Byram
8 - Did well to see out another 90 minutes in the space of a couple of days. Reliable and communicated well with Solomon down the left. Photo: Ben Roberts Photo
3. Pascal Struijk
8 - Dominated aerially, tidied up on occasion and held his positioning well despite not really being tested. Photo: Naomi Baker
4. Joe Rodon
8 - Stoke's opening chance of the evening aside, a solid, strong and uneventful display. Photo: Lewis Storey
5. Jayden Bogle
8 - Linked up well with Dan James all night and was a physical presence when needed to be. Photo: Barrington Coombs
6. Ethan Ampadu
7 - A few sloppy passes and a little bit of rust during the opening 15 minutes but soon shook that off to take control of the middle. Still getting back to his best. Photo: Ben Roberts Photo