The result piles further pressure on beleaguered West Ham manager Sam Allardyce, who received a vote of confidence from the club's co-chairmen earlier in the week.
After a promising start, the hosts were ahead within 13 minutes as Negredo volleyed home brilliantly from inside the area.
|VIEW FROM THE ETIHAD STADIUM
|By Tom Maston
If there wasn’t enough pressure on Sam Allardyce already, there certainly will be now. West Ham supporters voiced their opinions on the under-fire manager throughout the second half, and his position is beginning to become untenable.
His side lacked any ideas or belief, and the comparison between them and the free-flowing ease in which Manchester City played was more stark than many will have witnessed this season.
Many of the plaudits for City will of course go to Alvaro Negredo, though it was hard to find anyone who put a foot wrong. Manuel Pellegrini’s first piece of silverware in England may not be too far away.
Things went from bad to worse for West Ham when Negredo finished well inside the area after 27 minutes, with Toure adding a third before the break to put a rampant City firmly in control.
Negredo then completed his treble with a fine strike from inside the area early in the second half, before Edin Dzeko turned home Gael Clichy's cross with half an hour remaining.
And there was time for Dzeko to score a second with a powerful finish on 89 minutes to complete a thoroughly miserable night for the visitors.
Manuel Pellegrini recalled a number of his regular players following City's 1-1 draw with Blackburn Rovers in the FA Cup.
The likes of captain Vincent Kompany, Samir Nasri and Toure all returned for the hosts, while West Ham, beaten 5-0 by Nottingham Forest in the FA Cup, recalled Guy Demel, Joe Cole and Mark Noble.
Allardyce also handed Roger Johnson his debut after the defender arrived on loan from Wolves.
City threatened from the off and Pablo Zabaleta came close to opening the scoring after just two minutes when he almost got on the end of Nasri's cross.
The City faithful did not wait much longer for the opener, however, with Negredo putting City in front with a superb finish after an expertly-crafted Toure throughball, launched from within his own half.
That goal was the former Sevilla man’s 12th in his last 11 home games, and Negredo doubled City’s lead soon after, latching on to Dzeko's neat pass to slip the ball over the onrushing Adrian.
Dzeko should have joined his strike partner on the scoresheet nine minutes before the break but he fired over after positive work down the right from Nasri.
City did score a third before the break, however, as Toure burst through the middle and, with Johnson backing off, calmly sidefooted past Adrian to wrap up a dominant first-half display.
The onslaught continued three minutes after the break. After some slick play on the edge of the area, Silva's pass was deflected into the path of Negredo, who rounded off his second City hat-trick.
Toure then almost registered his second, curling a free-kick over the crossbar, before Dzeko kept up his record of scoring in every round of the competition by adding a fifth on the hour mark.
Thanks to almost constant pressure, City added a sixth through Dzeko as he fired home Aleksandar Kolarov's cutback as West Ham conceded at least five goals in two consecutive matches for the first time since October 2001.