Daniel Sturridge put the home side ahead in the 20th minute from the penalty spot, while Roberto Firmino doubled his team’s advantage towards the end of the second half.
Jurgen Klopp’s side were the better team from start to finish and entertained the Anfield crowd with a spirited, committed and skilful display.
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There were two moments of skill from the match, in particularly, that delighted the Liverpool supporters.
One was a beautiful turn to leave two Manchester United stars for dead - and the other, minutes later, was a sublime piece of footwork from Adam Lallana. (Scroll down to see both videos).
Video: Roberto Firmino skill
Video: Adam Lallana skill
Klopp wants repeat performance next week
Liverpool are now the overwhelming favourites to advance to the Europa League quarter-finals, but must finish the job at Old Trafford next week.
Klopp was thrilled with his side’s performance but warned his players that, in order to progress to the next round, they must produce the same type of performance at United’s home ground next Thursday.
"It was good, from the first second to last second, with only a few minutes in the second half when we lost control," the charismatic German coach was quoted as saying by Sky Sports. "2-0 is a perfect result. We would have liked to have won by more clearly, but there is nothing to criticise tonight.
"As a human being, I could really celebrate and say it is the best and greatest ever but I don't want to set a limit for them, I don't know how strong they can be.
"We are in a good position now and want to go to the next round but for this, we have to play like this again."
Klopp praises Liverpool fans
Klopp also praised the Liverpool fans, who combined to create a special atmosphere at Anfield.
"It was unbelievable," he added. "I want to say thank you to everyone who was involved. It was easy to enjoy from the first to last second.
"That was Liverpool as I knew it before I came here. It was really great.”
Liverpool could secure Champions League place
Winning the Europa League would see Liverpool secure a place in next season’s Champions League, although the Reds still have an outside chance of securing a top-four finish in the Premier League.
Currently seventh in the table, the Merseyside outfit are six points behind fourth-placed Manchester City with 10 matches left to play.
Will Liverpool win the Europa League this season? Let us know by leaving a comment below.