United made a flying start to the game, with Rafael and Antonio Valencia wreaking havoc down the right and quickly earning a corner, from which a poor clearance found Tom Cleverley. The midfielder's shot looked to be a certain goal, but Adrian pulled off an excellent save to prevent the hosts from taking the lead immediately.
It didn't take too long for United though - Welbeck continued his, er, red-hot form by puling off a quite excellent finish after being played down the left by Wayne Rooney, and using his left-foot to finish past Adrian from a tight angle.
Later on, some fine play down the left saw Januzaj exchange a one-two with Welbeck before bursting into the box on the right-hand side of goal, completely wrong-footing James Collins with a dummy and then curling a fine low finish into the far corner. Januzaj then marred the goal slightly however by being booked for a pretty terrible dive shortly after.
West Ham had hardly had a sniff in the first half, and United didn't really give them many chances bar a couple of set-pieces in the second either, although Collins went extremely close, but failed to get enough on his header from a corner.
Welbeck then sadly had to be withdrawn with what looked like a knee problem, with Moyes not wanting to take any chances. Javier Hernandez came in as his replacement, and should have had a goal himself, getting down the right channel and producing a smart finish from a tight angle, only for the goal to wrongfully be ruled out for offside.
Young coming on to replace Januzaj is a common but rarely popular substitution, but it paid an instant dividend here as Young scored with almost his first touch, collecting Rooney's lay-off to smash a brilliant effort into the top corner.
Carlton Cole then grabbed a consolation for the visitors after being played a mile onside by the substitute Alexander Buttner, slotting home through De Gea's legs to finish the scoring. Hernandez somehow managed to miss a remarkable chance from a short corner in the dying minutes, but in the end, United had to settle for just three.