A hat-trick from striker Sergio Aguero spared City an embarrassing exit as they fought back at the Etihad Stadium.
The SkyBet Championship visitors, who had won just twice in their last 16 matches, sensed an upset after Fernando Forestieri and Troy Deeney gave them a half-time lead.
That appeared to make a mockery of the pre-match odds which saw City, winners of the competition in 2011 and losing finalists in May, 7/2 favourites to win the cup while the Hornets were 33/1 just to win the tie.
City manager Manuel Pellegrini's half-time substitutions saw defenders Vincent Kompany and Pablo Zabaleta sent on with forward Stefan Jovetic added in the 57th minute.
Within two minutes City pulled one back when Aguero converted Aleksandar Kolarov's cross and after the Argentina international doubled his tally Kolarov added a third three minutes from the end but there was still time for Aguero to complete his treble.
Earlier, Liverpool, seven-time winners who last lifted the cup in 2006, were 2-0 victors at Championship side Bournemouth after goals from Victor Moses and Daniel Sturridge in either half.
Cup holders Wigan beat top-flight opposition Crystal Palace 2-1 in a minor upset at the DW Stadium.
The Latics were relegated from the Premier League after their historic cup win in May and only 14 places separated them from the visitors, who were a Championship side last season.
Cup final hero Ben Watson put his side ahead in the 36th minute and although Aaron Wilbraham equalised midway through the second half, James McClean quickly restored Wigan's advantage.
Fellow Championship side Birmingham threatened a surprise when Lee Novak gave them a 15th-minute lead at home to Premier League Swansea but two goals from Wilfried Bony in three second-half minutes turned things around and decided a 2-1 win.
Non-league Kidderminster put up a brave fight at Capital One Cup finalists Sunderland but went down 1-0 to a fifth-minute goal from 19-year-old Charis Mavrias, his first for the club since joining in the summer.
Premier League sides Hull, Southampton and Cardiff all made it safely through.
Matty Fryatt scored both goals as the Tigers beat League Two Southend 2-0, Guly Do Prado and Sam Gallagher scored in the Saints' 2-0 win at home to Yeovil while Frazier Campbell's solitary strike was enough to defeat Championship side Bolton 1-0 at the Reebok Stadium.
In the all-Championship clash, Simon Church scored early in the second half as Charlton won 1-0 at Huddersfield.
Brighton won 3-1 at Port Vale as Rohan Ince and Solly March scored either side of Chris Robertson's equaliser before Jonathan Obika wrapped up victory.
League Two Rochdale lost 2-1 at home to Sheffield Wednesday, who had goalscorer Joe Mattocks sent off, as they could not force an equaliser after Michael Rose had pulled one back. Oguchi Onyewu had scored the Owls' second.
In the late game, Everton comfortably avoided an upset at Stevenage with a 4-0 victory marred by an horrific injury to Bryan Oviedo.
The Costa Rica international was carried off on a stretcher and immediately taken to hospital where reports suggested he had suffered a double fracture to his lower left leg.
Two goals from Steven Naismith were followed by efforts from substitutes John Heitinga and Magaye Gueye as Everton eased into the next round.
Not a nice feeling to be 2-0 down at home by the break - but it's a great feeling knowing your side can come back and score four goals in the last 45 minutes. Whatever the odds looked like, if you put money on Watford at 33/1 you still lost it.- onstandby