The Irons went ahead the 34th minute but in extremely controversial fashion as Manuel Lanzini converted from a goalmouth scramble but only after a crucial intervention from Jarrod Bowen who had been in an offside position.
The goal stood despite a lengthy check from VAR and both sides then squandered some fine chances to add to the scoring before the Hammers finally put Leeds away deep in second half stoppage time as Bowen finished off an Irons counter attack.
Whites head coach Marcelo Bielsa was without nine players due to injuries - including the still absent Patrick Bamford - and the Argentine gave debuts to youngsters Leo Hjelde and Lewis Bate plus a first start to Sam Greenwood.
Graham Smyth, the YEP's chief football writer, hands out the scores.
. Leeds United again exited the FA Cup at the third round stage through Sunday's 2-0 loss at West Ham.
EARLY PRESSURE: Whites defender Luke Ayling clears Jarrod Bowen's short off the line in the opening exchanges of the third round FA Cup tie at the London Stadium.
. Illan Meslier
7 - Looked to be put off by an offside Bowen for the first goal and was left on a one-v-one with Bowen for the second having had to race back from attacking a corner. Made a couple of big stops. Photo by JUSTIN TALLIS/AFP via Getty Images.
. Luke Ayling
6 - Couldn't make a telling difference in the opposition half or stop West Ham from creating in his area of the pitch. Photo by Alex Pantling/Getty Images.
. Diego Llorente
6 - Some nice passes but came under a lot of pressure defensively, with a young centre-half next to him. Photo by Robbie Jay Barratt - AMA/Getty Images.
. Leo Hjelde
7 - Had the most difficult of tasks marking Antonio and stuck to it well. Couldn't always contain him but few can. Photo by JUSTIN TALLIS/AFP via Getty Images.
. Junior Firpo
6 - Another who struggled to get forward to any real effect. Forced off by the effects of a first half collision with Meslier. Photo by JUSTIN TALLIS/AFP via Getty Images.
1. Illan Meslier
7 - Looked to be put off by an offside Bowen for the first goal and was left on a one-v-one with Bowen for the second having had to race back from attacking a corner. Made a couple of big stops. Photo by JUSTIN TALLIS/AFP via Getty Images.
2. Luke Ayling
6 - Couldn't make a telling difference in the opposition half or stop West Ham from creating in his area of the pitch. Photo by Alex Pantling/Getty Images.
3. Diego Llorente
6 - Some nice passes but came under a lot of pressure defensively, with a young centre-half next to him. Photo by Robbie Jay Barratt - AMA/Getty Images.
4. Leo Hjelde
7 - Had the most difficult of tasks marking Antonio and stuck to it well. Couldn't always contain him but few can. Photo by JUSTIN TALLIS/AFP via Getty Images.
5. Junior Firpo
6 - Another who struggled to get forward to any real effect. Forced off by the effects of a first half collision with Meslier. Photo by JUSTIN TALLIS/AFP via Getty Images.
6. Robin Koch
6 - Didn't stand out but didn't have a bad game, just couldn't give Leeds control or the level of protection the back line needed. Photo by Stu Forster/Getty Images.