Suarez is unquestionably top. As John W Henry, the man who pays his wages, tweeted during the game, he is "a magician". The striker is someone, like Gerrard, Wayne Rooney or Mesut Ozil who creates a frisson of electricity whenever he comes near the ball.
Like Zlatan Ibrahimovic, there is a realisation that he can be a bit of an arse. Ibrahimovic confessed to such in his autobiography. Suarez acknowledged it in a television advert for a Uruguayan company that saw him fall outrageously to the ground, claim credit for everything and put his fellow workers off their game.
Both, however, reward their backers with the kind of magic that makes football worthwhile. Few who were in Brussels in midweek could forget Ibrahimovic's four goals for Paris Saint-Germain and the same can be said of Suarez's hat-trick at Anfield yesterday.
He, too, might have scored four. There was an outrageous overhead kick on to Boaz Myhill's crossbar and the last kick before he was brought off to a standing ovation saw the West Bromwich Albion keeper save at full stretch.
It would be wrong to say the Uruguayan was the difference between Liverpool and West Bromwich Albion Martin Skrtel cleared off the line, while Daniel Sturridge also struck a thoroughly bruised crossbar and scored the best goal of the afternoon, a beautiful chip into the net in front of the Kop.
Suarez had just hurled himself with wonderful theatrically into the penalty area, a result of the slightest of tugs from Gareth McAuley, when he showed his other side, the kind that merits his ranking alongside Kenny Dalglish and Kevin Keegan as one of Liverpool's great No 7s.
There were four West Bromwich defenders around him as he advanced toward the Anfield Road End. None got close. He skipped past Jonas Olsson and surgically drove his shot into the corner of the net.
And yet the two other goals were in their way even better because, whatever Suarez is, he is not renowned as a scorer of great headers. The leap to meet Aly Cissokho's cross was reminiscent of Keegan in his pomp, but what was remarkable was that the header came from the edge of the area and flew past Myhill as if had been delivered by his boot. It struck the same corner of the net but six feet further up.
Ten minutes after the interval, Gerrard delivered a free-kick from the left. Suarez twisted his body as he leapt to meet it and the hat-trick, his fourth for Liverpool and his first at Anfield, was complete.
"It was our best 90 minutes of the season," said his manager Brendan Rodgers. "I thought we looked a very good team today. The front two are as good as it gets and we have players like Philippe Coutinho to come back.
"Once I got the commitment from Luis in the summer I knew what he would do. He is not just a great player, he is a tireless worker and I knew, if he stayed, he would work as he has always done."
West Bromwich Albion were not ordinary opposition. They had beaten Liverpool in Rodgers's first match as manager; they had won here in February and beaten Manchester United at Old Trafford last month. Perhaps, most significantly, they had conceded just twice away from the Hawthorns this season.
They kept attacking even when three goals down and, when Billy Jones was brought down, earned a penalty which James Morrison converted. They had not come to Merseyside on a damage-limitation exercise, although they would return to the Black Country in pain.
Liverpool had used the match programme to celebrate the 50th anniversary of their battle hymn. You'll Never Walk Alone was released by Gerry and the Pacemakers right after a 1-0 win over West Bromwich that sent Bill Shankly's side fifth in the table, two points behind Manchester United.
They finished that 1963-64 season as champions. That may be beyond them this time round, but it is worth recalling another line from Ferguson's autobiography, that even in the depths of Liverpool's decline he could "feel their breath on my neck from 25 miles". For the moment, his successor can see only Liverpool's back.
Liverpool (4-4-2): Mignolet; Johnson (Kelly, 62), Skrtel, Toure, Sakho, Gerrard (Allen, 86), Lucas Leiva, Henderson, Cissokho; Suarez (Luis Alberto, 89), Sturridge.
West Bromwich Albion (4-2-3-1): Myhill; Jones, McAuley, Olsson, Ridgewell; Yacob (Brunt, 69); Amalfitano (Morrison, 45), Sessegnon, Anichebe; Anelka (Long, 69).
Referee: Jon Moss.
Match rating: 8
Man of the match: Suarez (Liverpool)