The first half was a relatively even affair, punctured in the final few minutes when Bobby De Cordova-Reid nodded home a rebounded Wilfred Ndidi shot.
Alejandro Garnacho's substitution at half-time was the shot in arm the Reds needed and, having his own effort blocked off the line seconds earlier, was instrumental in creating the equaliser ultimately knocked home by Joshua Zirkzee.
Just as it looked like United were heading for another FA Cup extra-time, Harry Maguire popped up at the back post to nod home a Bruno Fernandes header in the last few seconds of stoppage-time.
More to follow.