Liverpool displayed fluidity and poise to maintain 2nd place in the Premier League and reach the 40 point mark after the 18th game of the season.
The reds only crime was going behind early in the first half - against the run of play - and guilty of some more poor defending and goalkeeping. Jonathon Walters headed in from the near post after losing Dejan Lovren and goalkeeper Simon Mignolet should have done better.
Apart from that the reds were well worth the admission fee.
Klopp selected the same line-up for the third consecutive Premier League game - the first time he has been able to do it since joining the reds.
Despite a promising start the reds were behind after 12 minutes. The reds goalkeeping questions continue, Mignolet should have done better, but Walters should not have got the header away - Dejan Lovren guilty of failing to keep the Stoke man in check.
But the reds fought back strongly, and despite some comedy officiating from the referee's assistant, it was golden boy Adam Lallana who grabbed the equaliser - he pounced on a mistake by Glen Johnson.
With minutes remaining of the first half Roberto Firmino scored his first goal in 6 games, ending a rare barren spell for the Brazilian. James Milner feeding him a pass inside the area, and Firmino firing his shot in (via bouncing off both goalposts).
Second half the reds were fluid.
Henderson and Origi were heavily involved in Liverpool's third - Origi sliding a ball across the face of the goal - and Imbula was forced to put into his own net - Mane surely would have converted.
Daniel Sturridge and Emre Can were sent on in the 69th minute, and less than 60 seconds later Sturridge had scored the fourth.
He pounced on a terrible Ryan Shawcross backpass - rounded the keeper and fired into the empty net. His first league goal of the season.
Liverpool now have two tricky games to come, Man City at home in less than four days time and an away trip to Sunderland a further 44 hours later.