Jamie Vardy continued his familiar habit of scored against Liverpool by dispatching Riyad Mahrez's third-minute cutback – the England striker's seventh in his past five outings against Klopp's men.
Leicester held firm under relentless pressure before the interval and Liverpool's reward arrived during the second period, courtesy of two expertly taken strikes from Salah that take the Egypt winger on to 23 goals for the campaign in all competitions.
"It is a maximum satisfaction to win like this and on perfect days we win football games. Today was pretty much perfect," Klopp told BBC Sport. "When we were one goal down our reaction was the best I've ever seen in this situation.
"The crowd were unbelievable and we needed them to score these two goals.
"Mo was fantastic with his dribbling and his vision. I couldn't ask more from him."
Klopp added: "Staying in the game is the real deal of football in this league but I am happy for Mo, I am happy for the team because this group is a fantastic group of players.
"It's a good team performance and a well-deserved win."
"Of course, after a defeat it is a disappointment but Liverpool played their best," said Leicester manager Claude Puel.
"We did well to score first and we tried to keep that in the second half. We need to continue our work but it is important to concentrate on the game on Monday and forget this game to move forward."