The young Magpies struck twice in the opening 17 minutes of their Division Two clash, with Dylan Stephenson's close-range strike opening the scoring at Whitley Park before Crossley turned from provider to goalscorer with a delightful bending effort from the edge of the penalty area.
Stephenson's terrific lob extended Newcastle's lead in the second-half before Crossley rounded off the scoring, firing home from Stephenson's cutback, as Elliott Dickman's side secured their first league win of the 2022/23 campaign.
Crossley, who signed his first professional contract with the Magpies in July, told nufc.co.uk: "Everyone was shouting and celebrating in the changing rooms at full-time. We have training tomorrow but everyone is buzzing to go in and see each other.
"To score two goals was unreal and I was very happy with myself when the whistle went.
"For my first goal, I took a touch and nobody was coming to press me so I thought I'd try to get a shot away. The sun was in the goalkeepers' eye-line so I tried to bend it in and hope he'd struggled to see it and I was buzzing to see it come off.
"For my second, I knew I needed to be in that triangle in the penalty spot. I'd seen the right-back drop off onto the goal line and I thought why not pull back? The ball then came to me and when you have a chance like that, you have to finish it which I did.
"Getting the early goal is always good. I think it starts the team off well and we put the opposition under pressure which helped us to kick on and score more goals, which we did.
"We held the line well at the back and defended well to keep a clean sheet which was really important. In training all week, we have been working on defensive balls in behind and stopping them. I think for all the lads, especially the defenders and goalkeeper, they will be buzzing about that."
United's second-string quickly switch their focus to Papa John's Trophy action on Tuesday night when they travel to the Eco-Power Stadium to face League Two side Doncaster Rovers in their opening Northern Section Group E clash.
After losing their opening three Premier League 2 fixtures, Crossley believes the convincing win against their Derby counterparts has arrived at a key time for the squad ahead of facing Rovers' first-team and is hoping to contribute further for United's youngsters.
The 18-year-old winger, who primarily plays on the left flank, added: "It's really positive going into the next game, a big one, against Doncaster. This result has got everyone back together. We'd lost a few games which we felt we didn't deserve and tonight's win is what we needed ahead of Tuesday.
"It's important for me to add goals to my game, especially as a winger. I like to either score or assist but goals is always want you want. You don't feel much better after you score and then you can't complain when you've won too. I'll be going home happy!"
