City effectively sealed their place in the final at Wembley with another one-sided demonstration of their attacking potency, Edin Dzeko with two and Yaya Toure joining Negredo on the scoresheet.
It was the second time in four days that West Ham have conceded more than five goals after they were knocked out of the FA Cup 5-0 by second tier Nottingham Forest on Sunday.
While City can now relax ahead of the return leg on Jan. 21, the result ratcheted up the pressure on West Ham manager Sam Allardyce, whose side are 19th in the Premier League.
Providing City safely negotiate the second leg, they will face Sunderland or Manchester United in the final on March 2.
The omens were stacked in City's favour with the match pitching the Premier League's highest scorers against a defence which had conceded 13 goals in four games since Christmas.
It was eight years since West Ham had last won at City and few predicted that their injury-ravaged squad could get a positive result.
Bookmakers were offering better odds on City winning 5-0 than any West Ham victory and even Allardyce pre-empted the clash by saying a draw would be a great result.
It did not take long for the gulf in class to emerge.
West Ham's defensive fragility was exposed after 12 minutes as Negredo was allowed to run unchecked between central defenders to latch on to a long ball forward from Toure, which the striker dispatched into the bottom corner on the volley.
The Spaniard doubled the lead after 25 minutes, starting the move with a tidy flick to strike partner Dzeko before running on to the Bosnian's return pass and finishing off with a perfect first touch and precise finish into the top corner.
The tie was effectively made safe on 39 minutes when Toure picked up possession in his own half, changed gears and strode 40 metres into opposition territory.
West Ham's defenders backed off into their own box, allowing the hulking Ivorian time to pick his spot and drill home a low finish.
The interval was a brief respite for the visitors who fell further behind three minutes after the break when Negredo completed his hat-trick with a fizzing side-foot effort with the game having settled into training-ground tempo.
Dzeko gave the scoreline an embarrassing look when he maintained his record of scoring in every round of the competition.
He poked in City's fifth at the near post from Gael Clichy's cross after a fast-flowing move involving David Silva and Samir Nasri before firing his side's sixth into the top corner a minute from time.
