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.
1. Illan Meslier
6 - Made two particularly strong saves but was beaten far too easily for the decisive free-kick, albeit Shelvey's strike took a slight nick on the way in.
2. Luke Ayling
6 - Coped fairly well against class act Saint-Maximin and sent in some good crosses going forward but with no takers in the box.
3. Diego Llorente
6 - Produced some lovely raking passes and strong defending only to then foul Manquillo for the free-kick which led to the winner.
4. Pascal Struijk
7 - Immense in last weekend's victory at West Ham and another commanding performance with some big clearing headers, tackles and interceptions.