Brazilian Fabinho was left out of the starting XI by Klopp and his decision was justified when Roberto Firmino headed a fine opening goal after 16 minutes.
They could have doubled their lead but Mohamed Salah and Sadio Mane proved wasteful and Lucas Moura took advantage to equalise in the 70th minute.
Fabinho was introduced seven minutes after the equaliser and helped the hosts wrest back control of the games before Tony Alderweireld turned into his own net in the 90th minute to hand Liverpool a vital three points.
“A proper impact,” Klopp said when asked about his £40million summer signing. “He only had to play 15 minutes against a tired side but he was brilliant. He won a lot of really good balls and passed the ball.
“First half we had very good moments but not enough. The boys who started the game did really well.
“And if you bring a sub, they have to make an impact, that is the plan. That’s why you bring them, and it was obvious with Fabinho.”
Klopp’s celebrations were unusually subdued as the Reds grabbed a dramatic late winner to leapfrog Manchester City and go back top of the Premier League.
Salah headed towards the far corner and Hugo Lloris palmed his effort away, only for Alderweireld to send it back in the other direction as it trickled over the line.
“I was relatively calm [after the winning goal] because it was a surprise, that situation,” the German added. “I saw the header and nothing else. I had no clue how the ball went in.
“I was not happy we conceded but I thought we needed it a little bit. In the first half we had fantastic chances and scored a wonderful goal.
“In the second half we looked heavy and couldn’t really play. They changed only a little bit. We didn’t adapt well.”
Liverpool will drop to second if title rivals City win their game in hand at home to Cardiff on Wednesday night, but Klopp insists his team proved they have the character to keep fighting until the end of the campaign.
“After Spurs’ goal we started playing again more. We had bigger chances,” he said.
“We compete with the best team in the world [Manchester City] and play against one of best in the world in Tottenham – it is a tough task. It is all good.
“We can play better football but in the first half we had a lot of good moments. In the second not that many but we scored – 2-1, brilliant!
“City last year were champions and are still pretty good. We have to fight like crazy. The crowd was outstanding. They were really here to push us and at the end it helped.
“It is only positive. I said there are 500 ways to win a football game and today was slightly ugly. Who cares?
“I am really happy we don’t have any breaks now. We compete with the best team in world for one position and that is really hard.”