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Arne Slot's team are now seven points clear of second-placed Arsenal in the Premier League table as they eye up this season's title.
Luis Diaz put the Reds ahead after 15 minutes - before Egypt star Mohamed Salah doubled Liverpool's advantage from the penalty spot soon after the half-hour mark.
Overall, it was a deserved win for the Reds, who can now go 10 points clear of Arsenal, at least temporarily.
Below are Liverpool's next five fixtures across all competitions - as well as those of title rivals Arsenal;
Liverpool - 1st (60 points)
February 19 vs Aston Villa (A) at 7.30pm - Premier League
February 23 vs Manchester City (A) at 4.30pm - Premier League
February 26 vs Newcastle (H) at 8.15pm - Premier League
March 8 vs Southampton (H) at 3pm - Premier League
March 16 vs Newcastle (N) at 4.30pm - Carabao Cup Final
Arsenal - 2nd (53 points)
February 22 vs West Ham (H) at 3pm - Premier League
February 26 vs Nott'm Forest (A) at 7.30pm - Premier League
March 9 vs Manchester United (A) at 4.30pm - Premier League
March 16 vs Chelsea (H) at 1.30pm - Premier League
April 1 vs Fulham (H) at 7.45pm - Premier League
Isaac Seelochan from The Liverpool Echo says: "I have a feeling Arsenal will cling on for a little while longer judging by their fixture list.
Nottingham Forest away is probably going to be their toughest test on paper, with games against Manchester United and Chelsea not going to worry a team of Arsenal's current calibre.
"It's why there will still be some nerves at Anfield, with Liverpool definitely having the trickier matches of the two teams.
Aston Villa away on Wednesday night will be a major test for Arne Slot's side, and Manchester City looked much more like themselves in a 4-0 win over Newcastle on Saturday afternoon.
"Overall, though, the Reds are in an excellent position, and Arsenal's striker shortage should give Slot's men more than enough confidence that even if the gap is closed, Arteta's team will struggle to keep up the pace until May."
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