Frank Onyeka could not prevent Midtjylland from losing their second Group D game following their 2-0 loss against Liverpool at Anfield.
Onyeka was in action for 90 minutes in the colours of the Danish club.
Starting without influential forwards Sadio Mane, Mohamed Salah and Roberto Firmino, Liverpool failed to register an attempt on target in the first half.
They broke the deadlock after Trent Alexander-Arnold played a neat one-two with Xherdan Shaqiri, the former teeing-up Diogo Jota to tap home in front of an empty Kop.
Midtjylland went close to equalising after a clever shot on-the-turn by Brazilian substitute Evander.
In the end, Liverpool finished with Salah, Mane and Firmino on the pitch, Salah doubling the lead with a stoppage-time penalty after the Egypt forward was brought down by Paulinho.
With group rivals Atalanta and Ajax drawing 2-2 in Italy, Liverpool have six points from two games, two more than second-placed Atalanta, who they visit next Tuesday.