Liverpool was struggling to capitalize on its overall superiority in the north-west derby until the Swiss international sealed the victory with 73rd and 80th minute strikes, both deflected past United goalkeeper David de Gea.
It was Liverpool’s first home win in the fixture since 2013, taking the Merseysiders one point clear in the standings over reigning champion Manchester City and with a 19-point advantage over United which is languishing in sixth spot in the EPL and with pressure mounting on manager Jose Mourinho.
“I’m completely over the moon about the performance,” said Klopp, whose side has emerged as genuine title contenders after a superb start to the season.
By contrast, Mourinho conceded that a top four finish was the best that his side could achieve.
“Win the title, of course not,” he told Sky Sports.
“We can still finish fourth, it’s not easy. For sure we are going to finish in the top six. The best we can get is fourth.”
A total of 36 goal attempts for Liverpool summed up the frenzied intensity of the home side which took the lead after a spell of prolonged pressure through a Sadio Mane strike on 24 minutes after he chested down a fine through ball from Fabinho before beating de Gea.
Other goals might have followed but United were provided with a lifeline before halftime as Liverpool keeper Alisson Becker, the hero of the midweek Champions League win over Napoli blundered, dropping a Romelu Lukaku cross at the feet of Jesse Lingard who gratefully accepted the opportunity.
The goal prompted United’s best spell. “After that the game was controlled,” claimed Mourinho, but the introduction of Shaqiri changed everything.
Mane burst down the left and his cross back eventually fell to the skilful midfielder whose fierce shot flew into the roof of the net via Ashley Young’s boot.
There was little response from United and with Liverpool swarming forward the third duly came seven minutes later.
Roberto Firmino’s flick set him up for a left foot shot that deflected off the lunging Eric Bailly for the clincher.
“It was very good day for me and to score two goals was just perfect,” Shaqiri told Sky Sports.
United has now conceded more goals (29) than the whole of last season in the EPL and despite Liverpool’s dominance Mourinho left French World Cup star Paul Pogba on the bench, instead introducing Marouane Fellaini at halftime to little effect.
While Mourinho may covet fourth place, his side is 11 points adrift of Chelsea, 2-1 winners at Brighton earlier Sunday, in the fourth and final Champions League qualifying spot.
Arsenal is fifth, three points adrift, after a shock 3-2 defeat at Southampton, ending a 22-game unbeaten run.