An initially pedestrian match exploded into life after a turgid opening spell when West Ham's Callum Davenport first deflected Stephen Ireland's shot off the line and then managed to chest Tal Ben Haim's follow-up effort on to the bar.
The Hammers were further rattled after 21 minutes as City's workrate increased and they won a free-kick 25 yards from goal. Elano was brought down while trying to go past Matthew Etherington and Martin Petrov stepped up to thump a curling left-footer on to the right post and out of play, with Robert Green rooted to the spot.
The defining moment of the game arrived after 37 minutes when West Ham's Mark Noble was given his marching orders for a second bookable offence when he scythed down Michael Johnson in front of referee Howard Webb just three minutes after an earlier booking.
Richards had to go off early in the second half after a sickening clash of heads with Ben Haim. It was fully ten minutes before Richards was stretchered off following lengthy treatment.
City didn't have to wait long for some good news, though.
Sturridge settled the City nerves with a fine strike to open the scoring on 64 minutes. The City youngster latched on to a botched clearance by Matthew Upson from Petrov's cross and lashed a rising shot into the roof of the net from ten yards out.
Elano made it 2-0 on 70 minutes after fine approach play by Vedran Corluka was rewarded when his cross to Stephen Ireland was quickly pulled back into the path of Elano, who rifled the ball inside the left-hand post.
There was a carbon copy goal six minutes later when Elano was in the penalty area again to finish when Ireland provided yet another cut back to the Brazilian.
After beating Lucas Neill along his own goal-line following a one-two with Corluka, Ireland fed Elano and the Brazilian hadn't forgotten what to do and duly smacked City's third goal into the same corner past Green.
Victory was certain but City themselves were down to ten men when Etuhu pulled up with hamstring trouble on 82 minutes as he chased down a through ball from Dietmar Hamann.
There was time for Ireland to flick a Julien Faubert goalbound effort behind with the back of his boot just prior to ten minutes of added time, but the result was never in doubt.