The draw for the fourth round gave the club’s Under-18s an added incentive to win the tie against the Tykes.
United’s Academy manager Joe Joyce: “We believe we’ve got some good young players.
“What we have to focus on is what we’re going to do, and the capabilities of our young players.”
Sunderland beat Ipswich Town on penalties last week in their third-round tie.
Barnsley Under-18s 1 (Alton)
Newcastle United Under-18s 2 (Armstrong 2)
Adam Armstrong''s second-half brace set up an FA Youth Cup fourth round tie at home to Sunderland.
The England under-17 international has been in prolific form at under-21 level and for his country, but these were his first under-18 goals of the season.
And they gave United a deserved win at Oakwell after a first half where Newcastle dominated possession but struggled to break down the Tykes.
With Gael Bigirimana travelling to South Yorkshire to watch the Magpies youngsters and former United players Paul Bracewell and Peter Ramage among the crowd, Dave Watson''s side forced a string of early corners before the hosts almost broke the deadlock after six minutes as Callum Pilkington stabbed just wide.
But from then on it was more or less one way traffic. First, Greg Olley played in Rolando Aarons who held the ball up and played in Alex Gilliead but the skipper shot wide, then Aarons found Armstrong but the frontman was denied from a tight angle by Elliot Chadderton.
The resulting corner, taken by Olley, was headed wide by Macaulay Gillesphey before Jonathyn Quinn teed up Armstrong to fire off target from the edge of the box.
Olivier Kemen was next to threaten, driving forward but seeing his thunderbolt tipped over the bar, and Quinn''s header from Olley''s flag-kick was blocked.
In a rare Tykes attack, James Bree crossed perfectly from the right but Pilkington was again unable to force home but the Magpies finished on top.
Gilliead found Quinn but his shot hit the side-netting, then from Olley''s wonderful slide-rule pass, Kemen was thwarted by the brave Barnsley keeper who was off his line quickly to smother.
Kemen then fired wide from distance before Ben Drennan ran from right-back but could only send a tame shot straight at Chadderton.
But United flew out of the blocks at the beginning of the second half, with Kemen having a shot turned behind and then another blocked.
And from the corner, again taken by Olley, Armstrong''s volley deflected off a red shirt and into the net.
The second soon followed as Drennan slipped the ball to the forward, who set himself before firing in off the post.
George Maris then had the ball in the net for Barnsley but was flagged offside before Newcastle missed a host of chances to kill the match off.
Gilliead blazed over following Drennan''s lovely turn and cutback, then Armstrong shot just wide and scuffed off target after great work from Aarons.
Substitute Daniel Barlaser and striker Quinn both came close and Aarons had a shot deflected wide before Harrison Biggins had a shot tipped over by Brendan Pearson in the Magpies goal.
The Tykes pulled one back in injury time to set up a nervous final few minutes as Jak Alton found the top corner but there will be a Tyne-Wear derby in the next round.
Newcastle United Under-18s: Brendan Pearson, Ben Drennan, Lubo Satka, Macaulay Gillesphey, Macauley Booth, Alex Gilliead, Greg Olley, Olivier Kemen, Rolando Aarons, Adam Armstrong, Jonathyn Quinn
Subs not used: Paul Woolston, Ryan McKinnon