Yet while the win even had Watford's bruised manager Walter Mazzarri cooing that Liverpool could lift the title for the first time since the creation of the Premier League, Klopp suggested everyone calmed down.
With Chelsea, fresh from their 5-0 hammering of Everton on Saturday, only a point behind and both the widely-admired Manchester City and Arsenal a further point adrift, Klopp reckoned it was far too early to get carried away.
"If somebody thinks being one point ahead after 11 match days is a big sign for the rest of the season, then I can't help this person," Klopp told reporters.
"We stay cool. It's the best position I can imagine but nothing else has happened.
"We knew that Arsenal drew against Tottenham but we didn't speak one word about the possibility of being top of the table.
"We saw Chelsea yesterday, quite impressive; Man City playing Barcelona, quite impressive; Man United, never write them off; Tottenham are a good side. There's a lot of really good teams around.
"For me it's more important that we look like a team who is able to win games."
They do. Liverpool became the first team to get to the 30-goal landmark in the league this season as Sadio Mane led the rout of Watford with a double.
It was the first time since their exciting title challenge in May 2014 that Liverpool had led the league but Klopp did warn that this was a very different outfit to the one that eventually finished runners-up to Manchester City after the infamous Steven Gerrard slip which gifted Chelsea a decisive win.
"I know the story two years ago when it was really close and everybody compares -- but this is not the team of two or three years ago," Klopp said.
"This is not the team (of) 25 years ago. We're completely new.
"When I came here I asked for time and patience and belief, and after 11 matches everyone's asking for guarantees and they are not there.
"The only thing we have is a pretty good football team."
(Reporting by Ian Chadband; Editing by Clare Fallon)
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