Two first-half goals by Darron Gibson settled the tie against a disappointing near full-strength Tottenham team.
Eight of the eleven United players who started that ill-fated Champions League defeat against the Turks lined up from the start, but their performance was indistinguishable from that debacle.
Gibson scored his first goal for the Carling Cup holders in the 16th minute.
Ji-Sung Park found Anderson racing down the left and the Brazilian cut inside past Michael Dawson to shake off a crunching challenge from David Bentley and find Gibson.
The 22-year-old Republic of Ireland international took the ball in his stride and scored with a sweet right-foot shot from 25 yards which went through the legs of Spurs defender Sebastien Bassong and into the bottom left corner of the net.
Gibson's second goal 22 minutes later was even better.
Park found Dimitar Berbatov on the left corner of the Spurs box. The Bulgarian touched the ball inside to Gibson, who worked a neat one-two with Danny Welbeck before curling a glorious right-foot shot from 25 yards into the top right corner of the net.
United's determination to prove their critics wrong was apparent from the start.
Anderson went close after only 48 seconds and this seemed to set the pattern for the rest of the game.
United squandered several chances - the worst miss coming at the end of the first half when Gabriel Obertan fired his low cross from the right too hard across the Spurs box, with Berbatov unmarked at the far post.
United had further chances to increase their lead after the break, while Tottenham's best chance of the game came in the 21st minute.
Jermaine Jenas fed Gareth Bale down the left.
Bale's deep cross to the far post was met by Jermain Defoe eight yards out, but his shot was superbly blocked by United defender Richie de Laet.