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The Reds looked set to endure another frustrating draw after wasting a flurry of chances throughout the contest until the Uruguayan sent a timely reminder to his critics.
The Premier League table-toppers now move seven points clear of Arsenal ahead of the Gunners' match vs Aston Villa in the evening kick-off.
Liverpool had goalkeeper Alisson Becker to thank after he was on hand to deny Bryan Mbeumo, while captain Virgil van Dijk also made a vital clearance in the dying embers.
Arne Slot's side looked set for third straight game without a win, but the substitute ensured that Liverpool ended their disappointing run and extended their lead at the Premier League summit.
Liverpool's supporters will be firmly fixated on the Emirates Stadium as they hope Unai Emery can come back to haunt Arsenal when his Villa team visit on Saturday evening (5.30pm).
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Here are the next five fixtures for Liverpool and their main title rivals in all competitions;
January 21 vs Lille (H) at 8pm - Champions League
January 25 vs Ipswich Town (H) at 3pm - Premier League
January 29 vs PSV Eindhoven (A) at 8pm - Champions League
February 1 vs AFC Bournemouth (A) at 3pm - Premier League
February 6 vs Tottenham Hotspur (H) at 8pm - Carabao Cup
January 18 vs Aston Villa (H) at 5.30pm - Premier League
January 22 vs Dinamo Zagreb (H) at 8pm - Champions League
January 25 vs Wolves (A) at 3pm - Premier League
January 29 vs Girona (A) at 8pm - Champions League
February 5 vs Newcastle (A) at 8pm - Carabao Cup
January 19 vs Southampton (H) at 2pm - Premier League
January 25 vs Bournemouth (A) at 3pm - Premier League
February 1 vs Brighton (H) at 12.30pm - Premier League
February 11 vs Exeter City (A) at 8pm - FA Cup
February 15 vs Fulham (A) at 3pm - Premier League
January 25 vs Southampton (A) at 3pm - Premier League
February 1 vs Fulham (H) at 3pm - Premier League
February 5 vs Arsenal (H) at 8pm - Carabao Cup
February 8 vs Birmingham (A) at 5.45pm - FA Cup
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February 15 vs Man City (A) at 3pm - Premier League
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