Manchester United comfortably overcame Barnet, whose task was made impossible when keeper Ross Flitney was sent off after two minutes for handball.
Liam Miller capitalised immediately, beating substitute keeper Scott Tynan from the resulting free-kick.
Kieran Richardson added a second on 19 minutes but Barnet then resisted until 51 minutes when Giuseppe Rossi struck.
Dean Sinclair got one back for Barnet, scoring from 12 yards, but United added a fourth through Sylvain Ebanks-Blake.
Barnet's night took just 100 seconds to go horribly wrong.
Flitney had advanced a few yards out of his area when he plucked a routine pass forward out of the air a yard before the ball had gone back into the area.
Referee Richard Beeby duly sent Flitney off - and the game was over as a contest.
The 43,673 crowd - the lowest at Old Trafford for six years - voiced their disapproval to no avail.
Striker Louis Soares was sacrificed without even kicking the ball as he made way for replacement keeper Tynan to come on.
And once Miller curled the free-kick into the top corner, the writing was on the wall for Barnet.
Manchester United manager Sir Alex Ferguson on Flitney's red card:
"Surely we need some common sense.
"Everyone was stunned by it. It shattered a young boy's dream."
Barnet boss Paul Fairclough:
"The decision was cruel and ruined two players' nights.
"Ross was distraught and we had to take off young Louis who, like us all, had been looking forward to this ever since the draw was made."
Man Utd: Howard, Bardsley, Brown, Pique, Eckersley, Martin (Gibson 75), Miller, Jones, Richardson, Ebanks-Blake, Rossi.
Subs Not Used: Park, Smith, Silvestre, Steele.
Booked: Miller, Jones, Eckersley.
Goals: Miller 4, Richardson 19, Rossi 51, Ebanks-Blake 89.
Barnet: Flitney, Hendon, Yakubu, King, Gross, Soares (Tynan 3), Lee (Batt 87), Sinclair, Bailey, Strevens, Grazioli (Hatch 75).
Subs Not Used: Charles, Graham.
Sent Off: Flitney (2).
Goals: Sinclair 74.
Ref: R Beeby (Northamptonshire).