Joao Pedro came close to pulling one back for the Hornets but his effort was saved by Zack Steffen. However, Watford did eventually find a way through in the 88th minute, with Joshua King converting from the spot after Braithwaite was adjudged to have fouled Cucho Hernandez.
Despite the late scare, City held on to secure their place in the next round of the Carabao Cup. Guardiola will be pleased with the performances of some of his fringe players, with Foden and Braithwaite impressing in particular.
Next up for City is a Premier League clash with Southampton, where Guardiola will be hoping to continue their strong start to the season.