Liverpool looked to hit back quickly, but Reds stopper Henderson superbly turned Sergi Canos' effort away from goal and Ryan Kent's low effort rolled a yard wide of the upright.
United continued to defend stoutly, and should have doubled their lead shortly before the interval. Ioannou surged forward and exchanged passes with Fletcher, only for the defender's near post effort to be brilliantly turned behind by Crump.
Less than 10 minutes into the second half, another golden opportunity went begging as O'Hanlon was caught in possession on the edge of his own area by Fletcher, but Rashford's powerful effort thundered against the crossbar and United were unable to pounce in the ensuing scramble.
Liverpool quickly capitalised on United's profligacy, drawing level just five minutes later when Jerome Sinclair clinically converted a penalty after being brought down by Ioannou.
That heralded a power shift within the game, as the hosts began to dominate proceedings. Henderson made a sharp low save from Canos, but was helpless 15 minutes from time when O'Hanlon fashioned space for himself and unleashed a fine 25-yard effort high into the United goal.
United rallied briefly towards the end but had to leave themselves susceptible to counter-attacks and, after Henderson had saved well from Sinclair and the impressive Sheyi Ojo had twice struck the woodwork, Sinclair fired in an injury-time clincher from 10 yards.
Liverpool: Crump, Randall, Maguire, Cleary, Williams, Chirivella, Canos, O’Hanlon, Sinclair, Ojo, Kent. Subs not used: Firth, Wilson, Hart, Marsh, Alexander.
Manchester United: Henderson, Riley, Barber, Borthwick-Jackson, Ioannou, Kehinde (Reid, 57), Redmond, Willock, Fletcher,