Spector grabbed two first-half goals before Carlton Cole's brace after the break completed the rout - United's first defeat of the season.
Victor Obinna had already had a goal ruled out for off-side before Spector headed the opener after 22 minutes.
And the former Red doubled the Hammers' advantage quarter of an hour later when he slammed a loose ball in.
The impressive Obinna set up both of Cole's goals after the break to leave United, who made 10 changes from the side that crushed Blackburn 7-1 at the weekend, well beaten.
And not only did a 4-0 scoreline not flatter West Ham, it could have been even more resounding.
And although he made chances, Ferguson didn't even have the excuse of having played a severely under-strength side with Ryan Giggs, Darren Fletcher and Anderson all involved.
Having produced their best display of the season against Blackburn, United turned in their worst in East London, on a night when Chris Smalling and Jonny Evans were torn apart by the pace, power and movement of Avram Grant's strikeforce.
And the Reds could have been ahead inside 10 minutes when Gabriel Obertan fired a low shot across Robert Green that the West Ham goalkeeper managed to turn on to the post.
Even then Javier Hernandez looked set to put away the rebound, only for James Tomkins to get his foot to it first. If West Ham rode their luck on that occasion, they felt aggrieved on 18 minutes when Obinna looked to have put them ahead with a deflected effort.
Celebrations
Upton Park erupted, but their celebrations were cut short when the goal was ruled out by referee, Mark Clattenburg Spector getting the final touch when in an offside position.
But it wasn't long until they were celebrating again when the same pair combined four minutes later to put Grant's side ahead.
With United stretched at the back, Obinna clipped a cross to the advancing Spector, who flicked a header past the reach of Tomasz Kuszczak.
United were rattled, Obinna coming close again and Ferguson out of his seat and on the touchline to berate his players.
He was right to be concerned as Spector struck again, this time picking up Fabio's block inside the box and flashing a shot past Kuszczak.
Obinna then had the United keeper at full stretch again with a low effort from 18 yards that had to be pushed away.
Ferguson threw on Federico Macheda for Bebe at half-time and the Italian made an immediate impact albeit inadvertently.
Getting in the way of Green's kick, the ball spun into the path of Hernandez but the keeper recovered in time to clear the danger. That proved to be United's last hope of a dramatic fightback as West Ham ran riot.
Obinna cut them open again on 56 minutes, crossing from the left for Cole to dive in and head past Kuszczak.
It was now a case of damage limitation and Ferguson brought on Rafael for Fabio in the hope of curtailing Obinna's influence.
It didn't work and a minute after coming on, Rafael was turned inside out by the forward, who crossed for Cole to score again on 66. After the hysteria of Saturday, it was back down to earth with a thud.
Source: Manchester Evening News
Source: M.E.N.