Georginio Wijnaldum and Roberto Firmino scored either side of half-time to hand the Reds a deserved lead before Erik Lamela set up a grandstand finish with a stoppage-time goal.
The visitors ultimately held on - despite a good shout for a Spurs penalty after Sadio Mane clipped the heels of Son Heung-min - to make it five wins out of five and Klopp was quick to hail his players after the match.
"That was very, very good," he told Sky Sports . "It was an intense job to do and the boys did it.
"We deserved to win that game today. Over 85 minutes we were really dominant.
"With and without the ball we caused them massive problems. The things they usually do usually work, but they didn't today," added Klopp. His side will now prepare to launch their Champions League campaign against PSG on Tuesday.
"The boys stuck to our plan today and it was really good - everybody worked so hard in what was a good performance.
"That was our best game of the season and the performance was much better than the result.
"We won the game and if we win at Tottenham it's a big result. The players did the job and they worked unbelievably hard, and I'm really proud of them."
Midfielder Wijnaldum, who scored Liverpool's first-half opener, conceded he got lucky with his far-post header after a training ground routine went wrong.
"It was a plan, we trained with it before. There was a misunderstanding between me and Joe [Gomez] because one had to stay. It was not the plan that two went," the Netherlands international told Sky Sports.
"I just thought I would head the ball as high as possible because there were a lot of players in the box. I had a feeling it was in straight away."