Just 49 hours separated the end of City's frantic 2-2 Premier League draw with Arsenal on Sunday and kickoff against the Hornets, resulting in Pep Guardiola making nine changes to his starting lineup - most notably handing 16-year-old defender Kaden Braithwaite his senior debut.
Watford, who also made nine changes, would have hoped to have kept things tight at the back early doors, but Man City needed just five minutes to open the scoring through Jeremy Doku, helped by an under-hit back-pass from Hornets defender Ryan Porteous in the build-up.
The Citizens doubled their advantage in the 38th minute when Matheus Nunes fizzed his first goal for the club into the bottom corner, after Watford's Kwadwo Baah had an equaliser disallowed for a barge into the back of Braithwaite.
Guardiola's much-changed side continued to dominate proceedings after the break and almost added a third when substitute Savinho fired a shot across goal and against the base of the post, before Jack Grealish was denied by Jonathan Bond at the near post.
Watford gave City a scare in the closing stages when Tom Ince curled a delightful left-footed strike into the top corner with four minutes remaining, and they pushed for a late leveller in stoppage time. However, the hosts held on to ensure they avoided a second successive exit in the third round after losing 1-0 at Newcastle United at this stage last year.
Man City will find out who they will face in the fourth round when the draw is made on Wednesday after Liverpool's match with West Ham United.
MAN CITY VS. WATFORD HIGHLIGHTS
Jeremy Doku goal vs. Watford (5th min, Man City 1-0 Watford)
Ryan Porteous under-hit his back-pass towards goalkeeper Jonathan Bond which allowed James McAtee to steal the ball and cut it back to Jack Grealish, who teed up Doku to stroke a right-footed shot into the bottom-left corner.
Kwadwo Baah Disallowed Goal vs. Man City (21st min, Man City 1-0 Watford)
Kwadwo Baah made a powerful run into Man City's box down the right channel and fired a superb low strike across goal and into the bottom corner. However, the Watford forward was deemed to have barged Kaden Braithwaite in the back before scoring past Stefan Ortega. Not even VAR could save the Hornets as the technology is not used at this stage of the EFL Cup.
Matheus Nunes goal vs. Watford (38th min, Man City 2-0 Watford)
Rico Lewis burst forward and poked a pass to Matheus Nunes, who took two touches before arrowing a sweet left-footed strike into the bottom corner - his first goal for the Citizens since joining from Wolverhampton Wanderers just over a year ago.
Tom Ince goal vs. Man City (86th min, Man City 2-1 Watford)
Giorgi Chakvetadze capitalised on Kyle Walker's poor attempted intervention and rolled the ball into the path of Tom Ince, who took one touch to set before curling a delightful left-footed shot into the top corner - his fourth goal in the EFL Cup this season.
MAN OF THE MATCH - MATHEUS NUNES
Matheus Nunes has struggled for regular game time at Man City since joining from Wolverhampton Wanderers last summer, but he took his chance in Guardiola's side against Watford and scored his first goal for the club towards the end of the first half - a sweetly-struck left-footed strike that fizzed into the bottom corner.
The Portugal international, who was a physical presence in midfield and linked up well with his teammates in the final third, could have scored a second after the break but was nevertheless a standout performer for the Citizens.
MAN CITY VS. WATFORD MATCH STATS
Possession: Man City 73%-27% Watford
Shots: Man City 24-5 Watford
Shots on target: Man City 8-1 Watford
Corners: Man City 10-1 Watford
Fouls: Man City 5-6 Watford
BEST STATS
WHAT NEXT?
Man City will now turn their attention back to the Premier League and are scheduled to face Newcastle United at St James' Park on Saturday lunchtime.
As for Watford, they will resume Championship duties with an encounter against second-placed Sunderland at Vicarage Road on Saturday afternoon.