Rangnick was sitting on the bench officially for the first time since taking over as interim manager until the end of the season.
If Spurs win their game in hand they will move into the top four places.
England international Raheem Sterling opened the scoring for the defending champions, when he met a cross with an impressive header, which was then complimented by a Bernardo Silva rebounded shot 25 minutes later.
Watford did bag a consolation goal when Cucho converted a short-range rebound deep into the second half, but that came after a second goal from Silva and confirmation of all three points for City.
Guardiola's side will be delighted that they were able to take advantage of some fortuitous results elsewhere in the league, as Chelsea allowed a 2-1 lead against West Ham slip and ultimately lost 3-2 to David Moyes’ side.
Jurgen Klopp’s Liverpool looked as though they may be dealt a similarly bitter blow against a stubborn Wolves side, had it not been for an injury time winner from Divock Origi to keep the Anfield side just one point off top spot.
Elsewhere, Southampton continued their lacklustre start to the new season with a dull 1-1 draw with Brighton and Newcaslte picked up an important three points against Burnley with a 1-0 victory at St James’ Park to lift them off the bottom of the table.
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