Just over two months ago Klopp's side appeared out of the running but a 10th consecutive league win briefly took them two points clear of their northwest rivals.
Next week the two heavyweights clash at the Etihad in a mouthwatering fixture that could potentially decide the destination of the title.
The two teams also meet in the FA Cup semi-finals later this month and both are involved in the Champions League quarter-finals in the coming week.
Quadruple-chasing Liverpool did not have the easy afternoon Klopp would have hoped for against Roy Hodgson's Watford, who are fighting for their lives.
The home side needed Brazilian goalkeeper Alisson Becker to be at his best to keep out Juraj Kucka before Jota nipped in ahead of Ben Foster to head in his 20th goal of the season midway through the first half.
But there was a nervousness around Anfield as the visitors refused to wilt and they even had a glorious chance to equalise in the second period.
Liverpool had to wait until a minute from time to get the two-goal cushion they desired when Kucka wrestled Jota to the ground from a corner.
Fabinho took responsibility from the spot and smashed into the top corner.
Klopp, who won the Premier League with Liverpool in 2020, said becoming English champions was his top priority after the Reds topped the table for the first time this year.
"The Premier League is the most important competition," said the German, whose side have already won the League Cup this season.
"A big two months (ahead) hopefully. This week can decide a lot about how May will be. The boys created a top-class basis and now we have to use it."
If City felt the pressure they did not show it.
Guardiola's men, chasing their fourth league title in five years, were ahead in the fifth minute at Turf Moor through De Bruyne.
Raheem Sterling controlled Rodri's cross-field pass and clipped the ball inside for the Belgian to rifle beyond Nick Pope.
City doubled their lead in the 25th minute when Raheem Sterling exchanged passes with De Bruyne before cutting the ball back for Gundogan to stroke home.
In the most eye-catching result of the day, Chelsea lost against Brentford after six straight wins in all competitions since owner Roman Abramovich announced his intention to sell the club.
The Stamford Bridge side took the lead when Toni Rudiger lashed home from long-range at the start of the second half.
But two goals from Vitaly Janelt and a first Premier League goal for Eriksen since his return to the English top-flight in a 10-minute spell turned the match on its head. Yoane Wissa scored late to complete the rout.
Wolves beat local rivals Aston Villa 2-1 and Leeds were held to a draw by Southampton while Brighton and bottom side Norwich drew 0-0.
Manchester United were set to host Leicester in the evening kick-off, seeking to put the pressure on fourth-placed Arsenal.