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 northwest 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.

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.

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.

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.

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.

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