Pep Guardiola’s side had won each of the last four editions of the tournament but after they were held to a goalless draw by the Hammers in 90 minutes, the tie went to spot-kicks.
Phil Foden fired wide from 12 yards with City’s first effort and West Ham remained perfect to secure a memorable cup win which occurred five years to the day of the last time the champions had suffered an exit in this competition.
Lucas Moura helped ease some of the pressure on Nuno Espirito Santo with the only goal for last year’s runners-up Tottenham in a 1-0 win over Burnley.
The Brazilian headed home a cross from countryman Emerson Royal in the 68th minute to settle a low-quality affair at Turf Moor.
Nuno still had to contend with discontent from the travelling faithful, who had chanted “Nuno where’s the subs?” before the breakthrough occurred but Spurs held on for a much-needed victory to progress into the last eight.
A much-changed Liverpool survived a tricky first half to beat Preston 2-0 with Carabao Cup specialists Takumi Minamino and Divock Origi on target.
Jurgen Klopp changed his whole XI from the weekend thrashing of Manchester United and saw the Sky Bet Championship outfit go close on various occasions during the opening half at Deepdale.
It remained goalless though until Minamino flicked home just past the hour mark and Origi wrapped up the victory with six minutes left.
Leicester required penalties to get past Brighton after an entertaining 2-2 draw on an emotional night at the King Power Stadium.
The tie took place on the third anniversary of the helicopter crash at the ground which killed the club’s chairman Vichai Srivaddhanaprabha and four others.
Harvey Barnes provided the perfect start after the Foxes had paid tribute to Srivaddhanaprabha with a minute’s silence before Adam Webster and Ademola Lookman traded goals during first-half stoppage-time.
Brighton forward Enock Mwepu ensured there was another twist in the clash with a second equaliser with 71 minutes on the clock but he later saw his spot-kick saved by Danny Ward in the shoot-out with Neal Maupay also firing over as Leicester triumphed 4-2 on penalties.
Brentford claimed a first ever victory at Stoke after Sergi Canos and Ivan Toney repaid the faith of their manager with goals in a 2-1 victory.
The duo were two of the three players who retained their starting berth from the defeat to Leicester and netted in the first half to put the Bees in control.
Former Brentford player Romaine Sawyers reduced the deficit after the break but Thomas Frank’s men held on to win and break their duck in Stoke, which put them into the last eight of the competition for the second year in a row.
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