This clash lived up to is billing as heavyweight scrap at Old Trafford with both sides showing their class in front of goal.
Neither side were able to create much in a frantic opening 20 minutes before a touch of inspiration from Mo Salah edged Liverpool ahead.
Roberto Firmino’s pass caught the United back line square and the Egyptian star kept his head to clip past Dean Henderson.
But Solskjaer’s side were not to be set back by that as rising star Mason Greenwood immediately levelled things up.
Marcus Rashford’s lofted pass escaped James Milner’s lunging header and Greenwood lashed past Alisson.
That high octane end to the first half set the tone after the break as Greenwood and Rashford swapped roles to put United in front.
Greenwood’s whipped pass forced an error from Rhys Williams on the counter and Rashford raced on to fire home.
But again the pendulum was to swing in the final 30 as the alert Salah reacted quickest to Milner loose to fire the Reds back level.
And just as the game looked destined for a manic final period both managers turned to their benches to tip the balance and it was Solskjaer that found the answer.
Portuguese international Bruno Fernandes has already established himself as a fans favourite at Old Trafford and it was his brilliant free kick that swerved United in Round Five.
Full Time on a dramatic afternoon at Old Trafford it’s Manchester United 3 Liverpool 2