United boss Ole Gunnar Solskjaer named a completely different starting XI to the side which had won 2-1 in the Premier League at London Stadium on Saturday, with Jarrod Bowen the only West Ham player to retain his place.
The visitors took an early lead through Manuel Lanzini in the ninth minute, with Juan Mata firing against the crossbar as United looked to respond.
Anthony Martial’s late effort was saved before Andriy Yarmolenko hit the post at the other end as the Irons closed out the final minutes to book their place in the next round.
Chelsea beat Aston Villa 4-3 on penalties after it finished 1-1 at Stamford Bridge after 90 minutes.
Timo Werner headed the Blues in front in the 54th minute for the German’s first goal in 11 games.
Villa, with the Duke of Cambridge watching on from the stands, were level just 10 minutes later when 19-year-old Cameron Archer nodded in from Matty Cash’s deep cross.
With neither side able to find a winner, the tie was settled by a shoot-out.
Villa captain Ashley Young hit the crossbar before Kepa Arrizabalaga saved Marvelous Nakamba’s spot-kick.
Although Chelsea defender Ben Chilwell rattled the crossbar and Emi Buendia then made it 3-3, Reece James lashed his penalty into the top corner to send the hosts through.
Tottenham also needed penalties to see off Wolves, who had fought back from 2-0 down to draw 2-2 at Molineux.
Nuno Espirito Santo, returning to face his former club, made seven changes to the side defeated by Chelsea on Sunday – and Tanguy Ndombele fired Spurs ahead in the 14th minute before Harry Kane doubled the lead after being played through by Dele Alli.
Wolves, though, pulled a goal back ahead of the break when defender Leander Dendoncker headed in from a corner and Daniel Podence equalised just before the hour which proved enough to send the tie to spot-kicks.
Neves missed his penalty and Dendoncker’s effort was saved by Pierluigi Gollini to put Spurs on the brink, and although John Ruddy kept out Pierre-Emile Hojbjerg kick, Wolves skipper Conor Coady failed to convert as the visitors went through 3-2.
There was no such drama at the Emirates Stadium as Arsenal beat Sky Bet League One AFC Wimbledon 3-0.
Alexandre Lacazette, captain for the night, converted a penalty in the 11th minute after Gabriel Martinelli had been fouled.
Emile Smith Rowe slotted in a second in the 77th minute, with Eddie Nketiah’s neat backheel completing a comfortable night for the Gunners.
Aaron Connolly scored twice in the space of five minutes in the first half as Brighton beat manager Graham Potter’s former club Swansea 2-0 at the Amex Stadium.
Alexis Mac Allister released Connolly into space on the left in the 33rd minute, and his angled shot deflected off Brandon Cooper past the Swans keeper.
The same combination soon realised the Republic of Ireland forward again, with Connolly this time drilling a low shot into the far corner.
Ademola Lookman scored his first goal as Leicester won 2-0 at Championship side Millwall.
The Foxes broke the deadlock five minutes into the second half when Lookman, on loan from Leipzig, knocked in a rebound after Kelechi Iheanacho’s long-range shot was saved.
Iheanacho added a late second to secure the Premier League side’s place in round three.
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