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The first match at Molineux between the teams, both in the last 32 of the Europa League and with plenty of tired legs, had ended goalless with United failing to land a single shot on target.
With closest rivals Leicester City suffering a shock 2-1 home defeat by Southampton, Roberto Firmino's goal sent Juergen Klopp's side 16 points clear at the top with a game in hand.
Arsenal earned their first win under new coach Mikel Arteta by comprehensively overpowering a stale Manchester United side 2-0 in the Premier League on Wednesday with goals from Nicolas Pepe and Sokratis.
Both clubs entered this season hoping to finish in the top four, but while Ole Gunnar Solskjaer has guided United to fifth place, just a point off the Champions League spots, Arsenal languish in 12th, 11 points behind fourth-placed Chelsea.
Fourth-placed Chelsea suffered a shock 2-0 loss at home to Southampton while Harry Kane and Dele Alli were on target as Tottenham Hotspur came from behind to beat Brighton & Hove Albion 2-1.
Liverpool took a giant step towards their first title since 1990 on Saturday when their 3-0 win at Bournemouth combined with Manchester United's 2-1 victory at Manchester City to leave the champions 14 points adrift of the Premier League leaders.
Even with strikers Mo Salah and Roberto Firmino warming the bench, Juergen Klopp's side had far too much firepower with Divock Origi scoring twice as Liverpool set a new club record of 32 league games undefeated.
The result left United top of the group on 10 points from four games, two ahead of Dutch side AZ Alkmaar who enjoyed a 5-0 away rout of Kazakhstan's Astana.
Liverpool's Anfield fortress was briefly shaken by Tottenham Hotspur but Juergen Klopp's side recovered to secure a 2-1 win and restore their six-point lead atop the Premier League on Sunday.
It was yet another Premier League game with VAR controversy which will continue to provoke debate about the system introduced this season.