With an average age of 22 and a half, this was one of the youngest sides that Sir Alex Ferguson has sent out in almost 19 years as United manager.
But the Red Devils were handed a clear advantage with only 100 seconds of the game gone.
In his enthusiasm to get to a meaningless ball Bees goalkeeper Ross Flitney handled a yard outside his penalty area.
Referee Richard Beeby applied the letter of the law and Flitney was sent off.
Barnet boss Paul Fairclough brought on Scott Tynan for midfield man Louis Soares, but it was the kind of hammer blow from which the League Two side never recovered.
From the resulting free-kick to the left of the D, United midfielder Liam Miller curled a tremendous right-foot shot into the top right corner of the net.
Tynan produced a magnificent one-handed save nine minutes later to claw away Kieran Richardson's blistering 25 yard drive.
But Richardson was not to be denied seven minutes later when he curled a delicious left-foot free-kick from 20 yards out on the right beyond both attackers and defenders and into the far corner of the net.
Richardson's pace caused Barnet problems again in the 25th minute when he cut in from the left and fired over a cross which rebounded off the top of the bar.
United were now totally in control and Adam Gross was forced to head a Giuseppe Rossi header from Miller's cross off the Barnet line in the 36th minute.
The home side effectively sealed victory six minutes after the interval when Rossi showed superb skill to control Lee Martin's low cross from the right before firing home left-footed from 12 yards.
Barnet, who had an 11th minute effort by Giuliano Grazioli disallowed for offside, pulled a goal back with a quarter of an hour to go.
United defender Gerard Pique slipped on the edge of his own area when he tried to control a loose ball and Dean Sinclair nipped in to round goalkeeper Tim Howard and score from ten yards.
United made it 4-1 in the last minute when Miller's long pass found Rossi clear in the Barnet box and he played the ball to his right for Sylvan Ebanks-Blake to slot the ball into the empty net from 12 yards.