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.
13. Willy Gnonto (sub)
6 - Strong in the odd duel he had to contest. Not much else to report as the game was all but won Photo: George Wood
14. Ao Tanaka (sub)
6 - Similar to Gnonto in the sense that all he had to do was keep things tidy and don't overcomplicate it, which is what he does Photo: George Wood
15. Mateo Joseph (sub)
7 - Bright and involved despite coming on with a quarter of an hour remaining. Photo: Barrington Coombs
16. Isaac Schmidt (sub)
N/A - Brought on during stoppage time to give Byram's legs a rest. Photo: Naomi Baker
17. Stephen Martin (referee)
6 - Few flashpoints to speak of, although could've taken a harder line with Stoke's Tom Cannon, or Junior Tchamadeu for the latter's foul on Byram. Photo: Stu Forster