A trip to Wembley for the semi-final was at stake, with the Whites not having played at that stage of the competition in 39 years, since losing 3-2 to eventual winners, Coventry, at Hillsborough in 1987.
Leeds settle quicker
The Hammers had been to the national stadium much more recently, though Nuno Espirito Santo would've been well aware that his side needed to up their game if they wanted to earn a place in the final four.
Their last FA Cup match saw them beat Brentford 5-3 on penalties after a 2-2 draw, but since that game, they hadn't won any of their last three games in all competitions.
With Leeds having already beaten their hosts earlier in the season at Elland Road, Daniel Farke's side knew that they had the measure of the East Londoners, and that probably accounts for their confidence in the opening exchanges of the match.
In the first two minutes, both Noah Okafor and Ethan Ampadu had shots on target, with Anton Stach's long-range effort going wide shortly after.
Superb finish from Tanaka
With 67% possession in the opening 15 minutes, Leeds continued to take the game to the Irons, with Ao Tanaka particularly prominent.
It would be the No. 22 who would strike first with a sensational piece of individual skill in the area after a pinpoint delivery from Okafor.
After scoring first in the FA Cup, Leeds hadn't lost a tie in over two years, since a 2-3 defeat to Chelsea on February 28th, 2024.
West Ham's game plan was clear, with Adama Traore winning eight of his 11 one-on-one duels before being subbed off later in the game.
However, the visitors coped admirably with containing the wide man, who managed only three touches in the Leeds box and one off-target effort in the 37th minute - just the second shot at goal from the hosts after Jarrod Bowen's in the 13th minute.
Backs against the wall for the Hammers
Farke's men kept up the pressure, with James Justin and Jayden Bogle each managing six touches in the Hammers' area, as Leeds pushed forward at every opportunity.
Stach's three shots before half-time were more than anyone else on the pitch had managed, too, indicating that unless the pattern changed, the visitors were odds-on to score a second goal.
Kyle Walker-Peters had already made four successful tackles before the whistle sounded for the break, and then attempted two more directly afterwards as Leeds again got straight on the front foot.
The ease with which Pascal Struijk was able to pass the ball around was remarkable, and an 82.5% success rate meant that he found a teammate more often than not.
Second Leeds goal sparks mass exodus
With Tanaka's best-in-class showing of 91.1% helping his colleagues to run rings around the opposition, it was a surprise that Leeds weren't making more of their opportunities.
Indeed, it was the Hammers who were coming on strong as the game approached the hour mark, Taty Castellanos hitting the woodwork and going close twice more, with Bowen and Axel Disasi also seeing efforts blocked.
Max Kilman, who had been excellent at the back for the hosts, and who would make more than a century of passes before the end of the match, was penalised with 20 minutes to play.
It took a VAR review of his challenge on Brenden Aaronson to see a penalty given in favour of Leeds, which was expertly dispatched by Dominic Calvert-Lewin - one of two shots the striker had on target - for his first FA Cup goal in five years.
Cue a mass exodus by the home fans who had clearly seen enough, but who would later come to regret that decision.
Forlorn hope for West Ham
Though Leeds would have six more attempts in the final 15 minutes, West Ham's controlled 79% possession gave them a platform for an unlikely late comeback.
Bowen's shot against the post in injury-time fell kindly for Matheus Fernandes to reduce the deficit, before Disasi's acrobatic effort in the 97th minute brought the Hammers level and sent the game into extra-time.
Ampadu and Aaronson were doing their best to stem the tide, with the pair involved in 37 one-one-ones between them; however, a consistent loss of the ball meant that the pressure only subsided when Craig Pawson blew the whistle for the end of normal time.
Six shots for West Ham in extra-time, including disallowed efforts and another Bowen shot against the woodwork, as well as an injury that forced off goalkeeper, Alphonse Areola, suggested it might not be the Hammers' day after all, and so it proved.
Though Areola's replacement, Finlay Herrick, saved Joel Piroe's penalty kick in the shoot-out, Lucas Perri then got down low to his right to keep out Bowen's effort.
Once Pablo missed again from the spot for the hosts, it was left to Struijk to smash his effort in off the post to send Leeds through.
