The home side, looking to build on their goalless draw with Portsmouth on Saturday, found themselves two goals down in the first quarter of the clash at Ashton Gate.
David James punched Carl Dickinson's long ball into his own net and Sean Murray slotted home from close range to give the Robins a mountain to climb early on.
Struggling City had chances to get back into the game but Ricky Foster, Jon Stead and Yannick Bolasie all failed to beat Tomasz Kuszczak in the Watford goal.
And the Robins' woes were exacerbated by the late sending-off of captain Liam Fontaine for a professional foul.
City manager Derek McInnes named an unchanged line-up following the stalemate at Fratton Park, while Sean Dyche made three changes to his Watford side.
Martin Taylor came in for Adrian Mariappa in defence, Chris Iwelumo replaced Britt Assombalonga up front and John Eustace made way for Prince Buaben in midfield.
The hosts started brightly, with Stephen Pearson smashing an early effort over the bar and Brett Pitman forcing Kuszczak into a save from a 25-yard set-piece, before Watford took the lead in the 15th minute.
Dickinson's aimless clearance downfield did not look likely to threaten the Robins' goal but James misjudged the flight of the ball and contrived to punch into his own net.
It was the third own goal scored by a City player in less than an hour of football at Ashton Gate, and the situation took a sharper turn for the worse for the home side five minutes later.
A smart Watford move ended with Troy Deeney forcing James into a save but Murray was on hand to scramble in his fourth goal in six matches.
City came close to reducing arrears just before half-time when Foster's left-footed volley was superbly saved by Kuszczak, while Pitman struck a free-kick high and wide as the visiting Hornets preserved their two-goal advantage through to the interval.
McInnes threw on Neil Kilkenny in place of Louis Carey at the break in an effort to spark a comeback from his side, but it was Watford who enjoyed the first sight of goal in the second period as Murray sent a 25-yard shot tamely wide.
Fifteen minutes passed without incident before Albert Adomah twice tested Kuszczak, but the Hornets' Polish stopper was more than equal to the winger's attempts.
And Watford almost put themselves out of sight moments later when Murray stabbed the ball goalwards following a goalmouth scramble only to see his effort cleared off the line and Iwelumo's drive was turned round a post by James.
City continued to create their own chances, and substitute Bolasie saw his strike tipped wide by Kuszczak, but their challenge ended with Fontaine's dismissal in the 78th minute after the centre-back hauled down Jonathan Hogg.
And the hosts' night was summed up when Stead could not convert after being played in by Kilkenny with 10 minutes remaining.