Sweeping from the Middle East to the Midlands without breaking stride, Liverpool took a big step closer to adding that much craved Premier League trophy to their recently acquired world crown. As in Qatar, so in Leicester, as Roberto Firmino opened the scoring here. But Liverpool did not settle for merely beating their nearest domestic rivals. They crushed Leicester as if issuing a warning to anyone who dares to challenge their supremacy.

James Milner scored from the spot before Firmino got another and Trent Alexander-Arnold lashed in a long-range shot to claim a superb goal to go with two elegant assists. This, then, was an almost feudal display, imperious rulers against bereft subjects. No one else has made Leicester look so puny this season.

Related: Alexander-Arnold the unexpected playmaker in Liverpool’s red machine | Barney Ronay

Granted, Brendan Rodgers’ team had lost a little momentum going into this game, collecting only one point from their previous two matches. But they are still a formidable side, a fact that Jürgen Klopp recognised by deploying his strongest available team. Rodgers, meanwhile, made one alteration to the lineup that started Leicester’s defeat by Manchester City, with Dennis Praet replacing Ayoze Pérez. That entailed a change of formation, with Harvey Barnes on the right while James Maddison operated from the left, and replicated the lineup Rodgers used at Anfield in October, when Leicester felt aggrieved to lose to a last-minute penalty by Milner. The plot failed and this time Leicester could have no quibble with the result. They were outclassed from start to finish.

It took two minutes for Alexander-Arnold to demonstrate his menace, as he sauntered into open space wide on the right and unleashed a swerving shot that Kasper Schmeichel had to bat away. Liverpool, showing no ill-effects from their travels, put their hosts under severe pressure, making Leicester look sluggish. Jonny Evans should have been punished in the sixth minute when Georginio Wijnaldum pounced on a casual pass-out from the back, but Mohamed Salah lifted a shot over the bar from the edge of the area. Salah went on to have an unusually ineffective game but key Leicester players were even less effective, with Maddison practically irrelevant in his outpost on the left.

Just as Leicester were beginning to find their feet, Liverpool nearly tore them apart. Naby Keïta cut through their defence with a pass from deep and Salah ran on to it, dodging a challenge by the outrushing Schmeichel. From an acute angle he tried to reproduce the geometric marvel that he summoned in the Champions League joust with Red Bull Salzburg earlier this month. But this time, even though he was able to use his preferred left foot,he could only dab the ball into the side netting.

Leicester sprung a dangerous-looking counterattack in the 20th minute but it transpired to be nothing more than an opportunity for Joe Gomez to demonstrate impressive speed by keeping up with Vardy before Alisson ran out of the box to quash the threat with that serene manner of his. Then Liverpool asserted their supremacy at the other end. Alexander-Arnold collected the ball in an unfamiliar position on the left but treated it with his customary finesse, dropping a superb cross over Ben Chilwell and into the path of Firmino, who nodded home from close range.

Leicester were still reeling from that when they gave up another opportunity. Schmeichel remained vigilant enough to deny Sadio Mané, who should have given him no chance from eight yards. But by now Liverpool were utterly dominant. Leicester made it to half-time thankful they trailed by only one goal.

The half-time team talks did not exactly inspire a transformation but Leicester did, at least, muster their first shot of the game in the 46th minute, Youri Tielemans’ drive from the edge of the box ricocheting off Gomez and out for a corner. However, Liverpool pressed so intelligently and intensely that Leicester struggled to make it out of their own territory.

Related: Liverpool’s dismissal of Leicester shows they will be hard to stop, says Rodgers

Alexander-Arnold cantered forward to deliver another fine cross in the 52nd minute, but Ricardo Pereira made sure Andrew Robertson did not get on the end of it. Moments later Robertson dispossessed a defender near the Leicester corner flag and crossed for Firmino, who missed from six yards.

Praet flashed a shot from distance just wide as Leicester tried to retaliate but, as they attacked more, Caglar Soyuncu twice had to stop Salah from profiting from counter-attacks. The Turk was entitled to feel satisfied when Salah was substituted. But seconds later Soyuncu inadvertently handled the ball from a corner by Alexander-Arnold. Milner hit the penalty down the middle. It was his first touch.

Soon Firmino highlighted the chasm between the teams by making it 3-0 from a cross by Alexander-Arnold. And then the young full-back emphasised the point by ramming a superb low shot into the corner of the net from over 20 yards.