Klopp's men had defeated struggling champions Chelsea 3-1 last month but an own goal from Eliaquim Mangala and two beautifully worked strikes by Philippe Coutinho and Roberto Firmino, all in the first 32 minutes, put them on their way to an even more impressive triumph on the road.
City's returning Argentine striker Sergio Aguero, a minute before halftime, produced a brilliant curling effort to threaten just briefly the possibility of a comeback win that would have taken them back to the top of the table.
Yet Liverpool, whose eye-catching Brazilian Firmino squandered a couple of other opportunities to seal the one-sided triumph, looked largely in control and completed the rout with a thunderous, if unlikely, 81st minute strike from Martin Skrtel.
It was a well-deserved win, full of zest and attractive football from the visitors which left Liverpool's Adam Lallana enthusing: "We didn't give them a second on the ball. Going forward we looked very dangerous, it was great fun!"
Having lost just once in eight matches since Klopp took over from Brendan Rodgers, Liverpool have moved up to ninth in the table on 20 points, eight points behind leaders Leicester City.
"It feels perfect! The game was not perfect but it was very good," Klopp told the BBC. "We played with big passion and that's the most important thing for us.
"The good news is that we can do better. We have quality, we could have more goals. The boys can believe now that they are stronger than many people think.
"We took our chances and made our goals. They were brilliant goals," Klopp added, evidently purring at how intricate interplay led to collector's items from his brilliant Brazilians Coutinho and Firmino.
It was a far cry from Liverpool's disappointing first defeat under Klopp at Anfield against Crystal Palace last Saturday.
"We need to stop slipping up at home," Lallana said. "These big wins go unnoticed if you lose at home but today is a great platform and hopefully we can kick on."
(Writing by Ian Chadband; editing by Toby Davis and Ken Ferris)
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