The 25-year-old had not scored in the league since November but was in the right place to finish after a neat one-two between Harvey Elliott and Alexander-Arnold.
Substitute Elliott was the creator for the second, feeding Nunez to cut inside and fire past Mark Flekken.
“As a striker, you get judged on goals, especially at a club like Liverpool,” said Reds captain Virgil van Dijk. “Today, he put his mark on the game.”
Liverpool also have a game in hand over injury-hit Arsenal, whose title challenge faltered once more at the Emirates. Gabriel Martinelli gave the Gunners a deserved first-half lead when Emi Martinez failed to prevent his effort crossing the line.
It was a similar story for Arsenal’s second as Martinez got a touch to Kai Havertz’s shot but could not keep it out.
Just when Mikel Arteta’s men seemed to be cruising, Villa hit back through Youri Tielemans’ header. The Belgian midfielder then hit the post with the chance to level for Villa seconds later.
The visitors did equalise 22 minutes from time when Ollie Watkins cushioned in Matty Cash’s cross off the underside of the crossbar.
Arsenal thought they had a late winner but Mikel Merino’s effort deflected in off Havertz’s hand and the goal was ruled out by a VAR review.
Bournemouth snapped Newcastle’s winning streak in stunning fashion as Justin Kluivert’s hat-trick fired the Cherries up to sixth.
The Magpies were looking to set a club record with a 10th consecutive victory in all competitions but were thoroughly outplayed by the visitors, who are themselves now on an 11-game unbeaten streak.
Kluivert, son of former Newcastle striker Patrick Kluivert, scored a hat-trick of penalties earlier this season at Wolves.
This time, all three of his crisp finishes came from open play as Bournemouth were rampant at St James’ Park.
Milos Kerkez added a fourth in stoppage time as Andoni Iraola’s men closed to within one point of fourth-placed Newcastle.
Bournemouth have never qualified for European competition before, and Kluivert said that is the goal for an ambitious squad.
“Why not dream big, and let’s see where we can end up?” the Dutch international proposed.
Leicester lost their seventh consecutive Premier League game as a 2-0 home defeat to Fulham edged Ruud van Nistelrooy’s men closer to a return to the Championship.
Emile Smith Rowe and Adama Traore were on target for the visitors, who move up to ninth.
Crystal Palace are up to 12th after a third win in four games thanks to Jean-Philippe Mateta’s double in a 2-0 win at 10-man West Ham.
Mateta opened the scoring early in the second half before Konstantinos Mavropanos’ red card gave the Hammers a mountain to climb.
The Frenchman then sealed the points from the penalty spot late on.