Norwich must hate the sight of Luis Suárez, but the feeling will certainly not be mutual. The Liverpool striker has now scored more Premier League goals at Carrow Road in 2012 than he has at Anfield as he followed up a hat-trick on his first visit to Norfolk with another treble as the Reds ran riot to end Brendan Rodgers's Premier League duck with his new club in emphatic style.

"It was a masterclass of finishing," said Rodgers of a striker who has now scored six goals in his past six games, but even Suárez's wonderful individual show could not overshadow a ruthless team display that suggests this season's Liverpool will be among the Premier League's great entertainers. The Uruguayan benefitted from a fluid midfield that controlled the game, pacy penetration from the wings and a Norwich side befuddled into incompetence. Shoddiness from the visitors in the latter stages took some of the gleam off the scoreline, but this was an impressive Liverpool performance and a result that was desperately needed.

An early-season fixture list that has been nothing short of vicious meant this fixture had assumed a significance it would not otherwise have been attributed. In the league it had been Liverpool's worst start since 1903 and while victory at The Hawthorns in the Capital One Cup had at least given Rodgers a first domestic win as Liverpool manager this trip had assumed season-starts-here status. If that holds true then what a start it was. "It's not a surprise because our performance level has been very good," said Rodgers, who went to say that his side's "relentless possession" was key in securing their first league win of the campaign.

He named Liverpool's youngest Premier League XI since the 2003-04 season, with first league starts for 19-year-old right-back Andre Wisdom and 18-year-old Spanish forward Suso, but it was one of the older hands who proved pivotal. Suárez took 68 seconds to send minds reeling back to his previous visit in April, slotting home after a poor clearance had dropped loose on the edge of the area.

Midway through the first half Suárez should have had a penalty after tangling with Leon Barnett. Rodgers had phoned Mike Riley to air his grievances about referees and the head of Professional Game Match Officials Board might have been getting another call had subsequent events not proved the decision no more than incidental. It could have been very different had Simeon Jackson not blasted Norwich's best chances of the half over the bar moments later.

As it was Suárez doubled Liverpool's lead eight minutes before the break with the pick of his bunch. As Norwich attempted to pass the ball out from the back – from a goal-kick won after Suárez had placed a shot miserably wide when clean through – the striker robbed Michael Turner, nutmegged him, then thumped a gorgeous effort with the outside of his foot past John Ruddy. Two minutes into the second half he turned provider, offering Nuri Sahin the simplest of tap-ins. The roles were reversed as Suárez completed his hat-trick, with the hugely impressive Sahin, given inexcusable amounts of time on the edge of the Norwich area, providing the pass from which his team-mate curled in his third. "It's a special day for him," Rodgers said.

Amid the joy, though, there was irritation for Rodgers. Steve Morison ensured it is now nine games since Liverpool kept a clean sheet in the league, slapping home after Pepe Reina failed to hold Russell Martin's shot. And, after Steven Gerrard's deflected shot had given Liverpool a fifth, the substitute Grant Holt blasted home a second consolation with three minutes to go after a mistake by Martin Skrtel.

That was Norwich's fourth goal in six league games and therein lies the problem for Chris Hughton. In replacing Paul Lambert with the former Newcastle manager, the Canaries have attempted to swap swashbuckle for solidity, yet here they came close to shambles. Chelsea and Arsenal are up next and will provide scant opportunity to exorcise the demons unleashed by this drubbing. "We need a response," Hughton said.