Wayne Rooney scored the only goal of the game to earn Manchester United an FA Cup fourth round tie with Fulham.
Rooney also missed a second-half penalty - the fifth time United have failed from the spot this season - as United survived a spirited second-half rally from West Ham.
Indeed, West Ham boss Sam Alardyce was left fuming after referee Phil Dowd somehow missed a clear handball in the penalty area from United defender Rafael.
It was Rooney's ninth goal of the season and extended a purple patch that began prior to his injury, since when Robin van Persie, Hernandez and Danny Welbeck have all impressed, underlining the strength within Alex Ferguson's striking department.
It seemed United's starting line-up was out to prove the wisdom of Ferguson's programme notes in which, whilst highlighting Van Persie's immense contribution this season, he stated firmly his side are not a one-man team.
Another of the men returning from injury, Anderson, provided the slide-rule pass for Hernandez to set up Rooney.
He also set up Nani, whose volley was curling in at the far post before it was brilliantly cleared off the line by Daniel Potts.
With West Ham's injury-hit side failing completely to plug the holes in midfield, United threatened to run amok.
No-one enjoyed themselves more than Ryan Giggs, who exploited the vast gaps to produce a virtuoso display that made him look far younger than 39.
With Red Devils chief executive David Gill confirming an interest in Crystal Palace wideman Wilfried Zaha, Giggs could soon have even more competition for his place.
As long as he is capable of contributions like this though, his United future seems secure.
Chris Smalling had a header saved by Jussi Jaaskelainen and Alexander Buttner's low cross struck a post as the pressure intensified.
Jaaskelainen was also called on to deny Rooney with a smart low save to his right.
It enabled West Ham to reach half-time still in contention, and Sam Allardyce to inject some much-needed self-belief.
They might have had a chance to equalise pretty quickly too, only for Rafael to escape a handball appeal thanks to the sympathy shown by referee Dowd.
Hernandez blazed a good chance over at the other end but the game was being controlled by the visitors, ensuring Chris Smalling and Phil Jones, United's 13th different central defensive combination of the campaign, were fully extended.
United were fortunate Rafael was in the right place to prevent Matt Taylor's square ball reaching Ricardo Vaz Te.
Taylor then curled an excellent chance over before Smalling managed to nick the ball away from Kevin Nolan just as the Hammers substitute was about to shoot from close range.
The hosts should have sealed their fourth-round spot after Jordan Spence handled Giggs' cross.
Rooney, though, blazed over, the effort sailing so high neither he nor his manager looked like they could quite believe it.
Something that definitely was believable was the woeful late tackle that earned Paul Scholes a booking as he flew in late on Taylor - not that it affected the outcome at all.