Fulham were full value for the lead that Aleksandr Mitrovic gave them five minutes into the second half, but the wheels came off with around 20 minutes left as manager Marco Silva, Willian and Mitrovic were all sent off.
It came after a Fulham corner became a United attack, with substitute Antony racing down the right and squaring for Jadon Sancho. He rounded Bernd Leno but saw his shot blocked on the line by Willian’s hand.
Chris Kavanagh signalled for a corner but was sent to the monitor by VAR Neil Swarbrick, and paused to send off Silva for dissent before he had even reached the screen.
The inevitable penalty decision and a red for Willian then came, but Fulham’s total loss of discipline was seen as Mitrovic raged at Kavanagh to earn his own early shower.
Bruno Fernandes sent Leno the wrong way from the penalty spot and two minutes later United led as Marcel Sabitzer flicked home Luke Shaw’s low cross for his first United goal.
Fernandes then lashed in United’s third in stoppage time as nine-man Fulham were overrun.
Twelve-time Cup winners United advance to face Brighton at Wembley while Fulham will count the cost of a day that will surely hurt their push for Europe via the Premier League with suspensions to follow.
It was a dramatic turnaround in a game in which Fulham had been the better team for most of the afternoon.
The absence of the suspended Casemiro and Fred – among the substitutes as Scott McTominay and Marcel Sabitzer started – told, as perhaps did United’s relentless schedule across four fronts this season as the hosts laboured against a Fulham side showing plenty of bite with Joao Palhinha back from a ban.
Early pressure saw David De Gea push Issa Diop’s looping header over, while Mitrovic wanted a penalty – and United defenders a yellow for diving – when he tangled with Lisandro Martinez in the box.
In between Willian fired narrowly wide and Tim Ream sent in a cross which would have only needed a slight touch to find the net.
United did not come to life until the final 15 minutes of the half after Marcus Rashford switched to the left and Sancho the right, but Leno foiled both Rashford and Sabitzer, while Wout Weghorst’s shot was deflected wide by Ream in first-half stoppage time.
The second half saw Fulham retake the initiative. Antonee Robinson’s curling shot was tipped over by De Gea, forcing the first of three corners which culminated in Mitrovic firing home after Diop flicked on Andreas Pereira’s delivery.
Fernandes fired wide from a Rashford cross before Ten Hag sent on Antony for McTominay, and the Brazilian was key to the Fulham meltdown that followed.
Antony almost added a third as he danced his way towards goal three minutes from time, but although he got around the keeper he was off balance before the ball was whipped away.
But Fernandes added the final flourish in stoppage time, lashing home a powerful strike to send United into the semi-finals for the first time since 2020.