The Brazilian ace, supposedly unsettled after a summer being chased by the mighty Barcelona, certainly looked back to his stunning best here.
Underlining just why the Spanish giants were prepared to pay £130million for his services, Coutinho made the first for Mohamed Salah before producing a trademark free kick to put Liverpool on course for a vital first win in five.
No wonder Klopp had ordered the Liverpool board not to cave into the pressure of a huge bid from Barcelona.
For when Coutinho ticks like this, more often than not the Merseysiders do too..
Even then it needed a remarkable second half penalty save from much maligned keeper Simon Mignolet to prevent Leicester snatching a point.
Having been dumped out of League Cup here four days earlier, Klopp’s Reds returned to the scene and took sweet revenge.
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Simon Mignolet saved Jamie Vardy's penalty to keep it at 3-2
And a first league win since crushing Arsenal before the last international break means they head to Spartak Moscow in the Champions League on Tuesday with renewed confidence.
For if not in contention at the top of the table quite yet, they at least have a reasonably healthy-looking 11 points on the board. That puts them joint fourth.
But if Klopp’s boys were chuffed at the final whistle, Craig Shakespeare’s Foxes were in the dumps.
This fourth defeat means they remain two places above the drop zone, with only four points – their worst start to a top flight season since 1994-95.
This was definitely a good moment to be facing Klopp’s misfiring team – as it had been in manager Shakespeare’s first game in the hotseat in February.
It was their England man Jamie Vardy who nearly set this clash alight after only five minutes.
Philippe Coutinho stuns fans with 15-minute cameo for Brazil
Having beaten the offside trap he was denied a sixth goal in four games against Liverpool by Simon Mignolet.
When the rebound fell to Riyad Mahrez he seemed certain to score… Only to blaze wildly over.
Amazingly, that was not the worst miss of the half – or even a frantic opening 13 minutes.
For when Liverpool midfielder Emre Can smacked the post from 20 yards out, Salah somehow failed to bury into an open goal.
If Klopp feared such spurned chances would come back to haunt them – as had been the case in the Carabao Cup – he need not have worried.
Two minutes later, Liverpool were ahead. Coutinho clipped a beautiful cross to the far post and Salah made amends with a deft header.
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And that was the signal for the Brazilian ace to assume control of proceedings – and virtually put Liverpool out of sight in the process.
Leicester’s fierce, pressing approach was always likely to give away free-kicks in dangerous positions.
Which is exactly what occurred in the 23rd minute when Wilfred Ndidi fouled Alberto Moreno outside the box.
From there it was all about Coutinho’s expertise with the dead ball as he fired a quite stunning, curling shot into the top corner. Despite a despairing dive, Danish keeper Schmeichel stood no chance.
Leicester probably felt aggrieved to be two down – with some justification.
That mood was hardly improved five minutes before half-time when a remarkably tight offside flag ruled out a sharp finish from Shinji Okazaki. The replays suggested it was Harry Maguire at fault.
Mick Quinn slams Oxlade-Chamberlain's start at Liverpool
However, in time added on, the hosts’ energy was finally rewarded as Liverpool’s creaky defence once again fell apart.
Mignolet flapped at a corner and when Maguire bundled the ball back into the danger, Okazaki managed to scramble it home.
Liverpool players were furious with the officials for not awarding a foul on their Belgium keeper. But really that anger should have been directed at Mignolet.
Inevitably, the Foxes came out with guns blazing in the second period – only for Jordan Henderson to silence the home fans with a 67th minute effort.
Yet as quickly they had restored the two-goal advantage, they then threw it away.
Mignolet did brilliantly to stop Demarai Gray’s blistering volley but could do nothing to keep out Vardy heading in from close range.
Seconds later the Reds stopper went from zero to hero with the travelling fans in a mad minute of controversial action.
Firstly, he conceded a 69th minute penalty when, in a race for the ball with Vardy, he sent the Leicester man flying.
However, having escaped with only a yellow, Mignolet dusted himself down to save Vardy’s spot kick low to his right.
