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."
Rodgers also praised the quality of Sturridge's goal despite him being shunted out of the limelight by Suarez.
"You used to see goals like Daniel Sturridge's here years ago, top players like Kenny (Dalglish) but that type of goal was incredible," he added.
The Reds boss could also not resist a joke at the expense of Sir Alex Ferguson after his criticism of Gerrard's quality and Jordan Henderson's physical attributes in his autobiography.
"Steven is a top, top, top, top, top player," he stressed, over-emphasising Ferguson's comments.
"Jordan was outstanding, athletically he was very good and he is getting better all the time tactically."
West Brom boss Steve Clarke had seen enough of Suarez's quality as a first-team coach under Dalglish at Anfield to know the threat he posed but admitted they failed to deal with it.
"It was difficult three times," he said.
"We gave ourselves a mountain to climb as we started too slowly and by the time we got into the game we were 2-0 down.
"The first goal came from nothing, defensively it was disappointing, but the second is an unbelievable finish from the edge of the box and the fourth goal was also sublime - that finish put the icing on the cake.
"Some days you have to take your hat off to the opposition and say they were better and their front two caused us problems."
- Sports & Recreation
- Daniel Sturridge