Liverpool took the lead on 24 minutes through Sadio Mane but they were pegged back before the interval via Jesse Lingard – who celebrated his 26th birthday the day previously.
However, the introduction of Shaqiri changed the game in Liverpool’s favour as his two deflected strikes gave them victory.
It was indicative of the mentality of the two managers that Jose Mourinho sent on defensive midfielder Marouane Fellaini at half-time with the score at 1-1 while Jurgen Klopp turned to Shaqiri when that scoreline had not changed midway through the second half.
That proved to be the masterstroke as he scored twice, both via deflections, as Liverpool beat United for the first time in nine league meetings.
Even with a game to chase Mourinho decided £89million midfielder Paul Pogba was not part of the solution as the French World Cup-winner was an unused substitute.
The goals United conceded meant they have let in more in 17 matches (29) than they did in whole of last season and trail leaders Liverpool by 19 points – they are 11 off the top four.
Liverpool’s high-intensity start was such that it almost seemed they could take and use possession at will as even when United – who started with a back three which quickly became a back five – had the ball, which was infrequent in the first half, the Reds won it back with ease.
MATCH FACTS AND STATS
Liverpool: Alisson, Clyne, Lovren, van Dijk, Robertson, Mane (Henderson 84), Wijnaldum, Fabinho, Keita (Shaqiri 70), Firmino, Salah.
Subs not used: Sturridge, Moreno, Lallana, Mignolet, Camacho.
Goals: Mane 24, Shaqiri 73 and 80
Manchester United: De Gea, Darmian, Bailly, Lindelof, Dalot (Fellaini 46), Herrera (Martial 79), Matic, Young, Lingard (Mata 85), Rashford, Lukaku.
Subs not used: Jones, Pogba, Romero, Valencia.
Goal: Lingard 33
Booked: Dalot, Lukaku, Matic
Referee: Martin Atkinson (W Yorkshire)
Mourinho had seen enough and sent on Fellaini in central midfield for wing-back Diogo Dalot at half-time as he reverted to a back four.
It did little to change the momentum as Firmino’s toe-poke was parried by De Gea with the goalkeeper and Young blocking Keita’s follow-up, while Lovren had a header deflected wide.
Three minutes after coming on Shaqiri struck, his shot rifling in off the crossbar with the help of a Young deflection.
He was not finished there, seizing on a Firmino backheel meant for Salah to fire past De Gea, this time with the aid of a deflection off Eric Bailly.