The two teams were level at 3-3 heading into the final stages of extra-time at Old Trafford, with a penalty shootout seemingly going to be required to decide which side would advance to the semi-finals.
However, Amad came up with a last-gasp winner for the Red Devils, combining with Alejandro Garnacho before finishing into the bottom corner for just his second goal for the club.
The 21-year-old has struggled for opportunities since returning from a knee injury at the end of December, and Sunday's match proved to be just his third appearance of the campaign.
Amad was heavily linked with a January loan exit, but he remained at Man United, and the forward has opened up on his spectacular late winner in the seven-goal thriller with Liverpool.
«Dream come true. That goal will give me a lot of confidence and I want to continue like this. I'm very happy. The most important thing is to win this game,» he told BBC Sport.
«I wanted to give it back to Garnacho but I saw the defender and I have to go on my own. It is unbelievable, it is a dream for me to score the last goal for Manchester United.
»I want to say thanks to the supporters. It is one of the best games of the season so we want to continue like this."
Meanwhile, in a separate interview with ITV Sport, he added: «What a game! Today we deserved this win, we played very good, it was one of the best games of the season. It's the best goal of my life it's a really important moment.
»You need to believe in every single moment, this is football. When Garnacho gave me the ball I wanted to give it him back but it
Read on sportsmole.co.uk