The Uruguay international scored twice before half-time in the 4-1 win, added another 10 minutes after the break and after James Morrison had converted a contested penalty Daniel Sturridge applied the coup de grace with a delightful inch-perfect chip.
Suarez departed just before the end to a standing ovation - less than three months after accusing the club of reneging on a deal to allow him to join a Champions League side following Arsenal's £40,000,001 bid - and gladly reciprocated.
He departed Anfield with the match ball, his fourth in a Reds shirt, and Rodgers felt the performance helped put a lid on all the shenanigans of pre-season.
"It was a difficult summer for him but it was for everyone and we managed as a club and he has managed himself well and he has come out the other side performing as he always done," said the manager.
"I knew once I had got the commitment from him in the summer he has been great.
"He is a tireless worker and I knew if he stayed it was going to be the case of working in training as he's always done.
"I thought the front two were brilliant. Suarez's first goal was exceptional, we really exploited the space in front of their centre-halves and he showed wonderful invention and creativity to nutmeg (Jonas) Olsson before taking his shot early.
"The second was a good team goal, I thought we moved it well, the cross came in early and he's guided the header in fantastically well.
"His third goal is from a great ball from Steven (Gerrard) and he could've had more after hitting the crossbar.
"It was his first hat-trick here at Anfield, I think you have seen his commitment to the team and what we are trying to do.
"It was a wonderful performance. Magic."
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