Leeds squandered several good chances to go in front but were undone in the 75th minute as Jonjo Shelvey's low free-kick from the edge of the area sailed through the Whites area and past Illan Meslier with the help of a slight Magpies touch in the box.
In winning for only the second time this season, Newcastle brought themselves seven points behind the Whites who stay 15th, seven points clear of the drop zone.
YEP football writer Lee Sobot hands out the scores from an extremely disappointing afternoon at Elland Road.
7. Mateusz Klich
6 - Nothing wrong with his shift in the middle of the park, energetic and clearly extremely frustrated after being taken off with ten minutes left.
8. Raphinha
7 - Produced some outstanding pieces of skill such as when skinning Dummett but Leeds were unable to make the most of his creative flair.
9. Jack Harrison
6 - The odd good moment but largely very well marshalled by Trippier down that side of the pitch.
10. Rodrigo
6 - Served up some fine through balls but could not offer an end product himself and faded in the second half though lasted the full game.
11. Dan James
5 - Ran his socks off and produced a fine piece of sweeper play to mop up a Magpies counter attack from a corner but unable to provide what Leeds needed in the no 9 role and squandered United's best chances.
12. Tyler Roberts (sub)
5 - Brought on ahead of Gelhardt but unable to make any impact in the front line and lost the ball for the move that led to the crucial free-kick.