Elliott Dickman's side broke the deadlock in the last-eight tie through Jay Turner-Cooke's first-half volley before Ferguson, who joined the Magpies from Tranmere Rovers in June, doubled the visitors' advantage with an impressive close-range finish on the hour-mark.
United's second-string, who have won the competition a record 38 times, were cruising towards a fourth successive win in all competitions before the Colliers drew level with two strikes in five second-half minutes, following Karl Ross' looping header and Craig Spooner's drilled equaliser.
However, Newcastle's youngsters prevailed on penalties as Jack Young, Adam Wilson, Rosaire Longelo and Turner-Cooke all converted from 12 yards and after United goalkeeper Will Brown saved Danny Anderson's spot-kick, Nathan Carlyon confidently rolled home the resulting and decisive penalty.
"It's great to progress into the semi-finals," Ferguson told nufc.co.uk. "It's always nice to be playing in those kind of games and it's a great test coming into men's football with opposition like Ashington. They are always difficult and they were brilliant, fighting till the end and coming back from two-nil down.
"When we conceded the second goal, we gave them too much respect and they came strong, playing until the final whistle. When you come up against these teams who fight with you, get into you, it's always a test.
"It could have went either way on penalties but we managed to put them all away so we're happy.
"I believe we can win this tournament. It's always nice to get a bit of silverware but I feel these games are great for the boys' development and those who aren't playing. There are some good teams left in the competition so we'll aim to try and come away with the trophy."
Ferguson, son of former Magpies forward Duncan, admitted scoring his first goal for the Magpies was "an honour" and is determined to contribute further in the campaign for United's second-string.
The 18-year-old, who joined on a three-year deal last summer, has also relished the step up from youth level this term.
"Sometimes when things like that happen, it's just instinct," the Liverpool-born explained. "The ball came in from Ros (Longelo) from the wing and I knew it would be coming in. I controlled it on the swivel, spun and took it on my right foot.
"It was a great feeling and I really enjoyed it! There's been a lot of hard work behind it, with a lot of coaches helping me this season.
"It's been a massive step up for me this year because I've came from Tranmere and it's been a new learning curve. It's a great team and squad and fantastic to be involved in.
"I've been lucky enough to play in some league games and we have Dylan (Stephenson) up top too who is doing brilliant right now so I'm happy to help as much as I can."
