The Red Devils reached the final four last season – one of four successive semi-final cup competition exits – and progressed from a tough fifth-round clash on Tuesday evening.
Ex-United boss David Moyes’ West Ham side made life difficult on a bitterly cold night at Old Trafford, where substitute McTominay struck home Marcus Rashford’s lovely 97th-minute lay-off to seal a 1-0 extra-time win.
Andriy Yarmolenko was then forced off in a goalless second half as the match went to extra time, with McTominay firing in his seventh goal of the season to seal progress.
West Ham were able to call on Tomas Soucek after his red card against Fulham was rescinded, while United made six changes from Saturday’s frustrating 3-3 draw with Everton.
Ogbonna got in the way of the shot but could not continue afterwards, having been sandwiched between the forward’s boot and oncoming goalkeeper Fabianski.
The defender had several minutes of treatment before being replaced by Diop, with Aaron Cresswell throwing himself in front of a Mason Greenwood strike at a time when the Hammers were temporarily down to 10 men.
Donny Van De Beek saw a shot deflected over towards the end of a first half in which Diop and Martial required treatment after a nasty clash of heads.
The defender continued for the remainder of the opening period but came off at half-time, with the Hammers confirming on their match blog that he was “replaced as a concussion substitute”.
Ryan Fredericks came on for him and Ben Johnson replaced Jarrod Bowen as the visitors went to a back five, with Yarmolenko soon limping off injured to be replaced by former United youth prospect Mipo Odubeko.
There were more substitutions to report on than clear-cut shots, with Fabianski doing well to thwart Rashford’s close-range shot in a drab second period.
Both sides struggled to stamp their authority on the game and Dawson wasted a chance to snatch victory in stoppage time, failing to get clean contact on a corner as Wan-Bissaka cleared his header.
The latter quickly made an important contribution, winning the ball after Declan Rice’s heavy touch to start the match-winning move. West Ham failed to effectively deal with a cross and Rashford teed up McTominay delightfully to rifle home in the 97th minute.
Said Benrahma looked lively as West Ham pushed to draw parity, with the substitute glancing a header straight at Henderson in the second half of extra time.
Martial wasted the chance to add gloss at the death but victory was already assured.