MANCHESTER, England -- Amad Diallo scored deep in extra time after Marcus Rashford made amends for a bad miss to lift Manchester United to a breathless 4-3 victory over north west rivals Liverpool and into the FA Cup semi-finals on Sunday.

United's victory at Old Trafford kept alive their only hope of silverware this season and spoiled Liverpool's dreams of hoisting four trophies in manager Juergen Klopp's final campaign with the team.

Erik ten Hag's side will face Championship (second-tier) outfit Coventry City in the semis after they upset Wolverhampton Wanderers 3-2 on Saturday.

"Listen to the noise, you can tell what a big game it is, a huge occasion," Rashford told ITV. "I haven't had the season I wanted but nights like this at Old Trafford are what it's all about.

"We have to get something out of this season... it's a massive game in the history of Manchester United."

Scott McTominay gave United a 10th-minute lead but Liverpool turned the game on its head with goals three minutes apart from Alexis Mac Allister and Mohamed Salah before halftime.

Liverpool dominated the second half and should have put the game to bed, but United poured on the pressure late in normal time and Antony spun in the box before slotting home past two Liverpool players in the 87th minute -- the Brazilian's first goal at Old Trafford in over a year -- to force extra time.

Harvey Elliott brought the 9,000 travelling Liverpool fans to their feet in the 105th minute when his long-range rocket deflected off Christian Eriksen's foot and between Harry Maguire's legs into the bottom corner.

But once again 12-times FA Cup winners United -- who are four places below Liverpool in a Premier League season to forget for Ten Hag's side -- kept their foot on the gas.

"Super intense," Klopp said. "We used the time and adapted well. We were outstanding but we had to finish the game off and we didn't."

Rashford, who had missed a sitter late in normal time, made it 3-3 in the 112th minute, calmly slotting a picture-perfect pass from McTominay into the bottom corner before running to United's fans, where he was mobbed.

"Rashford is resilient, he keeps going, normally he finishes those moments but he kept going for another chance. That inspired the other players," Ten Hag said.

Then Alejandro Garnacho and Diallo charged up the field on a breakaway after a Liverpool corner with Diallo firing home the winner in the 120th minute to a deafening roar from the Old Trafford faithful, leaving Klopp looking stunned on the sideline.

"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," Diallo said. "You need to believe in every single moment, this is football."

Diallo was then sent off after receiving a second yellow card for his celebrations.

"We always have belief, the problem is we have not been consistent with our performances," United captain Bruno Fernandes told ITV. "We give 100% we always give everything but at this club we always have to have high standards. It's a part of the game to be criticised, that's why you play for Manchester United.

"This season has not been at the level we want but we want to improve. We have always said our goal was to get into the top four and try to win the FA Cup, we will do all we can for those goals. The FA Cup is a big trophy for this club."