Georginio Wijnaldum scored his first ever away goal in the Premier League to break the deadlock at Wembley before Roberto Firmino doubled the visitors' lead in the 54th minute.
Erik Lamela grabbed a goal with minutes to spare to set up a frenetic ending - where Spurs could feel aggrieved after not being awarded a penalty with seconds to go.
Although Jurgen Klopp will be curious as to why his side couldn't convert more of the many chances they created, the closing five minutes of today's game very almost undone what was a landmark win for Klopp's side. We need to improve a lot. Yes, we learned, the experience was that one game can be completely different to another. "I do not have the personality to wait for problems but I know they will come", Klopp said.
While Kane collected the Golden Boot in Russian Federation, the six goals came in his first three games and that was followed by a three-match barren run.
Liverpool are scheduled to play seven games in the next 23 days starting with the weekend's trip to Wembley on Saturday.
Four wins from four in the opening stretch of the season spoke well of Liverpool's ambitions without them ever quite hitting top gear, but the relative ease with which they dispatched Spurs counts as a statement. I don't know exactly at the moment, but it's something with his eye.
I had to look at the incident three times, then finally in slow motion to see if there had been contact.
The 26-year-old Brazilian came off after 74 minutes after a clash with Spurs defender Jan Vertonghen.
Thankfully, Firmino had some good news for fans after being released from hospital with the diagnosis being an abrasion of the left eye.
The Reds play host to Paris Saint-Germain on September 18 in the first round of the competition, and Klopp will have to ensure the squad is able to stay clear of any injuries.
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