Following the 3-0 win over Bournemouth which took Liverpool back top, Murphy said: "I thought it was a superb performance from him at a time when there were a few nerves about which is understandable given the last couple of games.
"He was tenacious, he was calm and at Anfield when it is a bit edgey, you need someone who is brave enough to play forward passes, to not worry about losing the ball. e did that really, really well.
"Bournemouth started the game really well. They had a good solid shape and Liverpool were finding it difficult to break them down - but he kept probing to give Liverpool the impetus to wear them down.
"He's starting to show the confidence and the calmness that Liverpool paid the money for.
Murphy picked out Fabinho as Liverpool's star player (Image: BBC )
Fabinho took some time to settle but is now proving his worth (Image: BBC)
"It was a flawless performance from him and he's probably made that position his own now - if he can stay fit."
The win put Liverpool three points clear of Manchester City thanks to goals from Sadio Mane, Gini Wijnaldum and Mo Salah.
"Some of the play was mesmerising and we could have scored more," said skipper James Milner. 'We're very lucky with the squad we have, the movement, link-up and understanding.
"The crowd was immense. There's not many better in the country when it is like that - it's like a 12th man."
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Fabinho has been instrumental for Liverpool in recent weeks (Image: GETTY )
A jittery Liverpool had drawn their two previous games - so this victory was just what manager Klopp had been demanding from his team.
He said: "We want to play convincing football and that's what we did. It was a very good sign today. We were creative. We had power and speed and we had some outstanding performances.
"All the goals were brilliant and the third was world class. Today we won in an impressive manner."