Liverpool needed the win after Manchester City beat Everton on Saturday - and it was substitute Shaqiri's rapid-fire double strike in the second half that gave Jurgen Klopp's side the three points they fully deserved.

Sadio Mane's 24th-minute volley from Fabinho's perfect delivery gave Liverpool the lead their lightning start merited, only for a dreadful error by goalkeeper Alisson to give United an unlikely lifeline before the break when he fumbled Romelu Lukaku's cross into the path of Jesse Lingard.

United barely offered an attacking threat but were frustrating Liverpool until Klopp introduced Shaqiri with less than 20 minutes remaining, with devastating effect.

Meanwhile, Paul Pogba remained an unused substitute on United's bench, Jose Mourinho opting instead to bring on Marouane Fellaini at the interval with his side short of inspiration.

There was an element of good fortune about both of the Swiss international's goals, one deflected in from close range and the other off Eric Bailly to beat keeper David de Gea - but one cannot begrudge Liverpool their victory against this desperately ordinary United side.

Liverpool's perfect week ends in style

Liverpool and Klopp faced a pivotal week in their season that would shape the immediate future - and they answered the questions posed of them in emphatic fashion.

The two tasks in hand were to get the victory they needed over Napoli to reach the last 16 of the Champions League then beat Manchester United to return to the Premier League summit.

Liverpool showed no hangover from their midweek efforts in successfully achieving that Champions League mission as they set about United with relish and went ahead through Mane - although Alisson's gift to Lingard stopped their momentum and gave Mourinho's side a chance of the point that seemed to be the extent of their ambitions.

Shaqiri's introduction changed all that to leave Klopp's men still unbeaten in the league and United 19 points adrift of their arch-rivals.

Liverpool are currently in the sort of mood where they believe anything is possible and the signing of Shaqiri has added to their collection of match-winners.

Mohamed Salah was quiet but Shaqiri stepped up in an impressive demonstration of the squad strength at Klopp's disposal.

Mourinho's Manchester United second rate

Manchester United and manager Mourinho may point to the two decisive deflections on Shaqiri's goals - but they would be fooling only themselves if they believe they deserved anything from this game.

Mourinho's gameplan, predictably, was one of physical strength and containment that Liverpool were dealing with dismissively until Alisson's blunder threw them off their stride.

The Old Trafford boss added further physical power in the shape of Fellaini at half-time but it was still Liverpool, albeit nowhere near as impressively as in the first period, who were positive and pushing, while United were passive.

Pogba was not even used and Anthony Martial arrived when it was too late - while Klopp brought on the maverick game-changer Shaqiri to make the difference.

The contrast was almost symbolic, demonstrating just how quickly United are heading in the opposite direction to this vibrant Liverpool side.

Man of the match - Fabinho (Liverpool)

Only Georginio Wijnaldum and Roberto Firmino made more passes for Liverpool than Fabinho, who was his side's heartbeat

'The strongest team won' - what they said

Manchester United manager Jose Mourinho on BBC Sport: "The strongest team won, but they won in the period when they were not stronger than us.

"In first 20 minutes of the first half there was a huge distance [between the teams]. They were better and stronger, they did everything better than us.

"But in the moment when the game was going down, Liverpool's intensity was dying, the centre-backs were shooting from 30-40 metres because they could not find spaces in a dangerous area."

Liverpool boss Jurgen Klopp, speaking to Sky Sports: "Over the moon about the performance. The way the boys played tonight was outstanding.

"We saw the line-up of United and their quality - how organised they were and they fight from the back. The plan was to be brave and chip the ball behind the lines.

"The first goal was if you could have drawn it would have been the goal. It's so deserved. Top, top first-class team."

Liverpool's biggest Premier League win over United - the stats

• Liverpool are now 19 points ahead of United - their biggest ever lead over them after the first 17 games of an English top-flight season (based on relevant points for a win rules).
• Liverpool have recorded their biggest Premier League victory over Manchester United at Anfield since also winning 3-1 in March 2011.
• Manchester United have now conceded 29 goals in the Premier League this season, one more than they did in the entirety of the 2017-18 campaign and the most goals they've conceded at this stage of a top-flight campaign since 1962-63.
• Liverpool recorded 36 shots against Manchester United - the most the Red Devils have faced in a Premier League match since Opta started recording shot data in 2003-04.
• Manchester United have picked up 26 points after their first 17 Premier League games, their worst points haul in the top-flight at this stage since 1990-91 (also 26 points).
• Xherdan Shaqiri has become just the second Liverpool player to score at least two goals in their first ever match against Manchester United for the Reds, and the first since Nigel Clough did so back in January 1994.
• Liverpool's Alisson has made as many errors leading to goals in the Premier League this season as Simon Mignolet and Loris Karius combined in 2017-18 (2).

What's next?

Liverpool travel to Molineux to play Wolves on Friday, 21 December (20:00 GMT), while Manchester United play away at Cardiff the following day (17:30).