Martial gave United the lead from the penalty spot on 32 minutes but Emre Can setup Coutinho with the all important equaliser before the half-time break.
The Reds managed to hold onto the draw in the second half and booked a place in the quarter-final stages of the competition in the process.
Manchester United v Liverpool
Stadium: Old Trafford
Manchester United confirmed starting lineup:
De Gea, Varela, Smalling, Blind, Rojo, Carrick, Fellaini, Lingard, Mata, Martial, Rashford
Subs: Romero, Darmian, Valencia, Williams, Schneiderlin, Schweinsteiger, Memphis
Manager: Louis van Gaal
Liverpool possible confirmed lineup:
Mignolet, Clyne, Lovren, Sakho, Milner, Can, Henderson, Lallana, Coutinho, Firmino, Sturridge.
Subs: Ward, Toure, Smith, Allen, Ibe, Origi, Benteke.
Manager: Jurgen Klopp
Goals: 38′ Martial, 45′ Coutinho