Diogo Jota put Liverpool ahead early in the second half, before Mohamed Salah sealed the win in stoppage time with a penalty that he won.
After a flat first half, Liverpool found a spark in the combination play between Xherdan Shaqiri and Trent Alexander-Arnold, with the latter setting up Jota's goal.
Alexander-Arnold later played a sublime through-ball to Salah, before the Egyptian was brought down unceremoniously in the box.
With Ajax and Atalanta only managing to draw their game in Bergamo tonight, the Reds are on their own on top of the group, and are well in control at this moment.
Here's how each player fared for the Reds in this game.
Liverpool Player Ratings
Alisson Becker - 7/10
He made a big save early in the game to deny Anders Dreyer a goal. He was commanding, and in control of high balls into the box throughout the game.
Trent Alexander-Arnold - 8/10
He was outstanding tonight. Alexander-Arnold was once again Liverpool's creator-in-chief, and it was a responsibility that he revelled in. He set up the opener, and played the ball for Salah to win the penalty as well.
Fabinho - 5/10
He didn't even manage to get past the first half hour, as the Reds' massive injury crisis deepened. They are no another centre-back down, with Jurgen Klopp hoping for the Brazilian's injury to not be too serious.
Joe Gomez - 7/10
He had a shaky start to the game, with a number of long diagonals going astray early in the game. But as he settled into things, he was assured defensively, with his positioning and pace being important assets.
Andy Robertson - 5/10
An uncharacteristically subdued night for Robertson, who really wasn't his usual self. He didn't get up and down the flank with the energy that he generally does. He was also caught out by Dreyer's runs a few times throughout the night.
Jordan Henderson - 6/10
Henderson only played the first half, where he tried to drive the team forward from midfield, in what was an insipid performance from the team. It is likely that he was only taken off as a precaution and not due to any injury concerns.
James Milner - 5/10
Milner did not have a very good game. He was sloppy in possession, conceded a few too many fouls, and didn't really add much to the Reds play in any aspect.
Xherdan Shaqiri - 7/10
Possibly the biggest positive for Klopp from this game was that Shaqiri played 90 minutes. He had a great game as well, setting up a chance for Milner in the first half, before playing an integral part in the build-up to the first Liverpool goal.
Takumi Minamino - 4/10
He was dreadful in possession, as the ball bounced off him and into Midtjylland feet several times. He needs to be more decisive on the ball.
Divock Origi - 5/10
He offered slightly more than Minamino, but still inadequate. Origi was started on the left flank, but in an attempt to mirror Sadio Mane's role, he kept trying to drift infield and lost possession.
Diogo Jota - 6/10
Another Anfield goal for Jota tonight - his first in the Champions League. His knack of being in the right place at the right time has been duly rewarded already for Liverpool.
Rhys Williams - 6/10
The youngster was calm on the ball, and read the game really well to make a few important interceptions for the side.
Gini Wijnaldum - 6/10
After replacing Henderson at half-time, Wijnaldum put in an assured midfield performance, which was strong in possession and very astute tactically.
Mohamed Salah - 6/10
His superb run was found brilliantly by Alexander-Arnold before Paulinho brought him down in the box. He tucked the penalty away with aplomb.
Sadio Mane - 5/10
Mane was quiet, and really didn't get down to his usual tricks on the left flank.
Roberto Firmino - 4/10
He only played the last ten minutes, but missed a golden opportunity after being set up by Alexander-Arnold.Published 28 Oct 2020, 04:13 IST