The Reds were looking for a flash of inspiration at Anfield as they sought to break down the dogged Red Devils’ defensive wall.
Jurgen Klopp’s side had dominated proceedings, but had seen an uncharacteristic mistake from Alisson allow Jesse Lingard to cancel out Sadio Mane’s opener.
Shaqiri was introduced to help deliver a spark, and the 27-year-old needed just three minutes off the bench to fire Liverpool in front and a further seven to put the result beyond doubt.
The summer signing from Stoke has proved to be a useful option for Klopp this season, with Van Dijk telling the Reds' website of his impact in a title-chasing side: “You can concede and it happened. The thing then was to bounce back and make sure we kept pushing, putting the pressure on them and being patient.
“That’s what we did and in the end, big Shaq came on and did the job for us.
“He is a fantastic player. He showed it since the first game against Manchester United in America [in pre-season]. He is something different and sometimes that’s a game-changer.”
While Shaqiri did the damage in the final third, Van Dijk did well to contain the threat posed by United striker Romelu Lukaku.
The Dutchman added on a vital victory which has lifted Liverpool back to the top of the Premier League table: “It was special.
“It was a long time ago that we won against them at home. We wanted to make it right and we wanted to show everyone that we’re doing pretty well.
“We had to be brave. We knew what we were going to face. They obviously have a lot of quality, especially up front, but we did well – we didn’t give them any chance to have clear options. It was a deserved win.”
While the Reds are delighted to have stretched their unbeaten start to the 2018-19 campaign and made their way back to the summit, Van Dijk insists nobody at Anfield is getting carried.
He added, with a trip to a dangerous Wolves side to be taken in on Friday: “We are on a good way [but] we’ve still got nothing – we need to keep going and take the positive notes out of everything that happened, and the things that could have gone better as well, analyse them and make sure we’re ready for Wolves.”