Mohamed Salah opened the scoring for the Reds, continuing his own streak of scoring against the previous four newly-promoted sides he's played against and marking his 51st goal for the club.
Sadio Mane doubled the Reds lead in the second half, and struck again after Callum Paterson had pulled one back for Neil Warnock's side, while Xherdan Shaqiri grabbed his first league goal for the club since signing in the summer.
Klopp's men also move ahead of Manchester City to take top-spot in the English top flight, with Pep Guardiola's side travelling to Tottenham on Monday evening.
26 - Liverpool have won 26 points in their opening 10 Premier League games this season (W8 D2 L0) - their joint-best start to a Premier League season after 10 games (also 26 in 2008-09). Threat. pic.twitter.com/4NsID1O9PA— OptaJoe (@OptaJoe) 27 October 2018
Liverpool have now won eight of their opening 10 league games, drawing the other two, with 20 goals scored and just four conceded; their joint-best return from the same sample since the 2008-09 campaign.
Next up for the Reds is a trip to the Emirates Stadium as they look to halt an Arsenal side who have won 11 consecutive games in all competitions, before a trip to Serbia to tackle Red Star once more.