The visitors, who put their 9,000 vocal travelling fans through the wringer on Sunday, can now make plans for Wembley later this month.
Their supporters will be there in even greater numbers, two years after Leeds last played at the national stadium - when they lost 1-0 to Southampton in the 2024 Championship play-off final.
Leeds, who won the FA Cup in 1972, have in fact lost on their three most recent trips to Wembley. They were beaten 1-0 by Doncaster in the 2008 League One play-off final and 3-0 by Aston Villa in the 1996 League Cup final.
You have to go all the way back to August 1992 for Leeds' last victory at Wembley, a 4-3 success over Liverpool in the Charity Shield, featuring an Eric Cantona hat-trick.
Leeds are back in the FA Cup semi-finals for the first time since 1987, when they lost 3-2 to eventual trophy winners Coventry City at Hillsborough.
For large parts of Sunday's game, they looked good value for their semi-final spot.
They nearly scored in the opening 90 seconds, but Noah Okafor was denied by Areola, before Tanaka's deflected shot bounced off the underside of the crossbar and over the line for their first goal.
Calvert-Lewin made it 2-0 with a penalty after Max Kilman caught Brenden Aaronson.
The late West Ham turnaround changed the flow of the game dramatically though.
Leeds had to defend for a lot of a frantic extra-time period, but in the end Daniel Farke's side, themselves not certain of avoiding relegation from the Premier League, came through.
Wembley awaits Leeds on the weekend of 25 April, with Chelsea standing between them and the final on 16 May.