The victory, sealed with a stunning goal from Emre Can, strengthens Liverpool's hold on third place in the table.
Jurgen Klopp's team have lost only one of their last nine Premier League matches and with only three fixtures left, Liverpool are three points clear of fourth-placed Manchester City, who have a match in hand.
And Hargreaves said: "For Liverpool, to finish the season third would be a great achievement.
"To finish ahead of United, City, all the money they have spent, Arsenal, to finish ahead of them... Liverpool are going places."
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