The Uruguayan hit a 35-minute hat-trick - his third against the Canaries - in a performance in which he dominated the Norwich defence throughout.
Here, Sports Mole analyses whether the result was a fair one.
On target 12
On target 5
Was the result fair?
The size of the win is probably harsh on Norwich, who did play their part, but there can be no questions over the destination of the points. Suarez was absolutely unplayable and proved that he really can score any type of goal. Norwich were certainly in the game, particularly at the start, but it was ripped away from them by the rampant Uruguayan.
Amazingly for a 5-1 win, not every player stood out. Brendan Rodgers picked the right team for this game, with Suarez allowed a free role up front to work his magic. Behind him, they had the right level of technical ability and competitiveness to get control of the midfield and once they went ahead there was only likely to be one winner. It was a much, much better showing than the one against Hull City.
The visitors were not nearly as bad as the scoreline suggested they were, they just don't have the type of player that Suarez is to call upon. The early gameplan was clear, to press Liverpool and try to create chances on the break to get an early lead. It was working well until Suarez's magnificent first goal, from which point the heads dropped and they allowed too much space at the back.
Sports Mole's man of the match
Luis Suarez: Could it have been anyone else? The Uruguayan put in one of the best individual performances that will be seen this season. He scored three top class strikes from outside the box, found himself room to fire in from a corner and also had the vision to set up the fifth. It was a one-man show.
There really was not a lot wrong from either side, so this is a tough decision. Jordan Henderson squandered a really good chance at 0-0, as he took too long on the ball before he shot and instead should have passed to Suarez. In the end it did not matter, but had Norwich gone up the other end and scored it could well have done.
Anthony Taylor did not have a lot to do in what was a very fairly contested game. There were a couple of frustrated tackles, but Taylor only used his pocket when required. There were one or two appeals for penalties and free kicks – particularly when Coutinho was clear and went down – but he turned them all down correctly.
Liverpool: The hosts remain at Anfield on Saturday and take on another struggling side in West Ham United, where a win would keep them in touch with the top three.
Norwich: It is marginally easier for Norwich in their next outing away to West Bromwich Albion at The Hawthorns. A win would see them move above the Baggies in the league.