The 22-year-old forward earned the man-of-the-match award after an impressive display and was a constant threat to the Liverpool goal, despite not scoring.
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Van Persie's effort was his 21st goal of the season as United maintained their lead over neighbours Manchester City and he was full of praise for his fellow forward.
Speaking to reporters after the game the Netherlands striker said: "Danny played really well. He was good in the combinations and played a big part in the first goal.
"A couple of times when we got the ball after they made a mistake he got in and I got in a couple of times.
"He has been brilliant. He is still young and has been really good in training as well.
"He has been working his socks off. He is a very positive guy. He loves to play football and did really well."