The league table doesn't lie, as Liverpool deservedly collected all three points against fierce rivals who are now 19 points adrift.
Nathaniel Clyne made a rare right back appearance as Liverpool try to deal with some defensive injuries in a game in which the midfield trio of Fabinho, Wijnaldum and Keita all excelled.
However, the United bus was providing stubborn resistance until Shaqiri came off the bench and added the two goals that gave this scoreline a sense of respectability.
The first half hour whizzed by in a flash but the reds had worked their way into a 1-0 lead.
There was high intensity and speed from the home team - with Fabinho in particular enjoying his best game in a Liverpool shirt. He was involved in the opening goal - when he lifted the ball into the path of the onrushing Sadio Mane.
Mane chested the ball down before pivoting and firing through David De Gea's legs.
As it happened: LFC 3-1 Man Utd
But ten minutes later Man United had drawn level, somewhat fortunately.
From a cross out wide, Alisson failed to catch cleanly and it bounced off his knee in to the path of Jesse Lingard who poked home.
The equaliser stifled the crowd and the reds lost their intensity for the rest of the half.
Half time arrived and there was a change from United. They brought on Fellaini for Diogo Dalot, who had picked up a first half yellow card.
Liverpool continued their dominance, camped in the United half, but as time wore on they began to revert to long attempts as their frustration started to build.
But in the 70th minute on came Shaqiri to replace Keita. It proved to be the game-changer.
In a seven minute spell the Swiss international found the space in just the right places to take advantage of panic in the United defence.
His first shot arrived after De Gea made a half clearance with his legs. His shot fired upwards in to the Kop goal taking a deflection off Ashley Young. Liverpool back ahead.
And he ensured there would be no fightback when he collected the ball from Firmino and drilled home a shot that took a deflection off Eric Bailly.
The Kop could relax and enjoy the sight of a 70th minute substitute searching for a hat-trick against United.
Liverpool return to the top of the league. 45 points from 17 games easily surpassing anything the reds have achieved before - even in any of their 18 title winning seasons.
Next up - Friday night at Wolves where the hope will be of securing the Christmas number one slot.
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