The Blues were at their scintillating best in the opening period when three goals from Yaya Toure, David Silva and an own goal from Havard Nordtveit within a 10-minute spell, ripped the hosts apart.
Further strikes after half-time from Sergio Aguero and a late fifth from John Stones made it a Friday night to remember for the Blues’ jubilant followers.
Now City fans can look forward to Monday night’s draw with hopes of another trip to Wembley next May still burning brightly.
The Blues’ first trip to the London Stadium couldn’t have gone much better.
City, with five changes made from the starting XI against Burnley, looked in the mood from the word go with West Ham allowing plenty of space and little or no pressure on the ball.
Pablo Zabaleta, playing in his occasional holding midfield role, almost opened the scoring on seven minutes when he drilled Silva’s cross towards goal only for Winston Reid to make a fine block four yards from goal.
Silva then forced a save from Adrian five minutes later before the hosts finally mustered a shot at goal as Mikhail Antonio’s shot was beaten out by Willy Caballero.
On 27 minutes Aguero’s smart volley on the spin was tipped over by Adrian as City continued knocking on the door – and five minutes later the door was opened as Angelo Ogbonna tangled with Zabaleta in the box and Michael Oliver pointed to the spot.
Yaya Toure continued his 100% record for the Blues as he expertly struck the ball home to give City the lead, but the Hammers should have been level with their next attack as Antonio’s shot was parried by Caballero into the path of Sofiane Feghouli who, despite the attentions of Gael Clichy, missed an open net from three yards out.
Just six minutes later, the game was all-but out of West Ham’s reach as a sumptuous move doubled the visitors’ lead.
It began on the right with Bacary Sagna who played intricate passes with Aguero and Silva before sending a superb cross that Nordtveit had little option other to toe poke the ball past his own keeper with Raheem Sterling sure to have scored had he not.
City effectively ended the contest within two minutes as Aguero and Sterling linked well to create space and the England winger had all the time in the world to pick out Silva who calmly slotted past Adrian to send the large travelling army into raptures.
The Blues wasted no time in further punishing the Irons, pressing the hosts back from the re-start and increasing the lead to four within five minutes.
Sterling continued to torment the home defence on the left flank before teeing up Yaya Toure who saw his low drive nonchalantly flicked home by Aguero who in turn finally edged into third spot ahead of Colin Bell in the Club’s all-time goal-scorers’ list.
There was only 50 minutes on the clock but, with the Hammers looking totally demoralised and the Blues taking their foot off the gas, there was little in the way of chances for either side until Stones completed the rout with his first goal for the Club on 83 minutes from a Nolito cornet - goal-line technology this time ruling in City's favour.
This was City at their very best and a fifth win in six games for Guardiola’s side, but it will be the style that the victory was achieved in that will have delighted the Catalan.
The referee’s decision to award a penalty for the challenge on Zabaleta was arguably the turning point, but it was just a matter of time before the Blues turned dominance into goals – the miss by Feghouli however could have made this tie completely different had the hosts, buoyed on by a partisan crowd, levelled soon after.
Star man: Raheem Sterling
Yet another sparkling display by Sterling who is currently in a rich vein of form. With a hand in four of City’s five goals, the Blues’ winger is looking better and better each week. There were numerous contenders for the award with Silva, Aguero, Zabaleta, Stones and Sagna all impressive.
What it means
City are in the last 32 of the FA Cup with the draw live on the BBC on Monday evening. It also means Fernandinho will now be available for City’s return to the London Stadium at the start of February with an extra FA Cup match to play.
There is now a nine-day break until the Blues’ visit Goodison Park where Everton await next in the Premier League.