Diogo Jota scored the 10,000th goal in Liverpool's history as they laboured to a 2-0 win over Awer Mabil's Midtjylland, maintaining their 100 per cent start in Champions League Group D.
After a woeful first-half display from Jurgen Klopp's side, Portugal forward Jota finished off a fine team move 10 minutes into the second period as he struck home from close range.
Socceroos winger Mabil played in a more defensive role than usual as he helped his side hold out Liverpool until the 55th minute.
Mabil made 18 passes and one interception in what is likely to be his toughest test in the Champions League this season.
Midtjylland's best chance fell to Brazilian Evander, who saw his shot on the turn flashed wide, while Liverpool missed further opportunities to increase their margin of victory.
However, a second eventually arrived for the hosts in added time, Mohamed Salah scoring from the penalty spot after he had been fouled by Paulinho.
Liverpool's victory helped them move top of the table after Atalanta and Ajax played out an entertaining 2-2 draw.