Neville's dismissal was the only downside for United who secured their passage thanks to goals from Danny Welbeck and Michael Owen, his third of the season.
Ferguson named a completely different starting XI to the one at Anfield and the youngsters rose to the challenge against Barnsley.
Had the Championship side shown a cutting edge to match their work rate it might have been a different story.
Ferguson handed a delayed debut to Gabriel Obertan, two months after the winger arrived from Bordeaux.
Obertan, 20, had proved his fitness with three games for the reserves after a nagging back injury and he should have marked the occasion by finding the target.
Up against former Old Trafford striker Mark Robins, now Barnsley manager, United needed only five minutes to make the breakthrough.
It was Welbeck who made his mark just as he did in the last round when he scored the winner against Wolves.
He was allowed a free header when Anderson delivered the corner and took advantage with a clinical finish.
Welbeck almost added a second five minutes later following a superb ball over the top from Anderson.
However goalkeeper Luke Steele prevented his side going two down by making a marvellous block.
Barnsley were again forced on the back foot in the 19th minute and Obertan should have scored when released by Owen. But again Steele stood tall and thwarted the Frenchman.
However the home side responded and skipper Stephen Foster was left cursing his luck four minutes later.
His header from Adam Hammill's corner beat goalkeeper Ben Foster but came back off the angle of the post and bar.
Back came United and Welbeck headed over the bar following a cross from Obertan in the 36th minute.
With only one goal separating the teams, Barnsley were by no means out of it. But there was disbelief around the ground when Daniel Bogdanovic's ball across the face of the goal seven minutes later was not picked up.
Owen then squandered a good chance in the 48th minute, scuffing a shot wide after being set up by Welbeck.
Barnsley were making a decent fist of it but Anderson should have done better six minutes later when he failed to test Foster.
Then substitute Zoran Tosic, who had replaced Welbeck, saw his effort narrowly clear the bar in the 57th minute.
Two minutes later Owen showed his class by making it 2-0, clipping the ball past Steele after getting between Foster and Darren Moore with Fabio supplying the pass.
However United were reduced to ten men in the 63rd minute when Neville was handed a straight red by referee Chris Foy for clattering into the back of Hammill.
Neville, who was on the bench against Liverpool, looked stunned at seeing his time on the pitch come to a premature end.
Anderson then twice came close in quick succession to pulling a goal back for Barnsley but both his headers were wayward.
However they had the bit between their teeth and were anxious to give a full house something to cheer about.
It was not to be though as United kept their shape and their discipline to move menacingly into the last eight of the competition.