Manuel Pellegrini's spared the beleaguered Hammers no mercy at the Etihad Stadium with Alvaro Negredo hitting a fine hat-trick.
Edin Dzeko struck twice and Yaya Toure was also on target as City added West Ham to a growing list of sides swamped at Eastlands this season.
Pellegrini's men have now scored 92 goals in all games this term, just one less than the club managed in the whole of their 2012-13 campaign.
Despite the clinical nature of the performance, Pellegrini still believes there is much more to come his side.
"I think the team always can improve," he said.
"Maybe we really played very, very well, that is why I am happy and also because we are balanced we didn't allow West Ham one chance during the game.
"But every game is different and we will see what this team can do in the future."
Negredo opened the scoring after 12 minutes with a thumping volley from an equally brilliant Toure pass.
He doubled the lead with another fine finish before Toure charged through weak Hammers defending for the third.
Negredo completed his hat-trick early in the second half before Dzeko twice got in on the act.
The formalities of the second leg still need to be played in a fortnight but fans will already be looking forward to a Wembley date with Sunderland or arch-rivals Manchester United.
Pellegrini said: "In football it is never finished but of course this is an important step towards playing the final at Wembley.
"We are very near the first final - but it is very important to continue in all the competitions playing the way we did today, and playing the way we did today is more easy if you want to win something."
Negredo's treble took him to 18 for the season following his £20million move from Sevilla last summer.
His form has offset the loss of top scorer Sergio Aguero through injury.
Pellegrini said: "Playing better than the way he did is not easy.
"He really played a complete game, not only because he scored three goals but because of his link with the midfielders.
"For me, it's not a surprise because I know the way he played in Spain for a lot of years and I think it's also important for Alvaro and Edin Dzeko to play well together, because maybe in other games they have not played as well as they used to."