First half goals from Sean Longstaff and Yasin ben El-Mhanni were enough for United's second string to record their first league victory of October on the month's final day.
They were gifted their opener after five minutes, when an error from Jordan McGhee in front of his own goal presented Longstaff with a one-on-one chance, which he took confidently.
And El-Mhanni's close-range strike - his first for Newcastle since his summer arrival - doubled his side's advantage midway through the half.
And football development manager Beardsley said that his team were deserving victors in their first St. James' Park outing of the season.
"For the first four or five minutes, to be fair to them, they played some good football, but I think the goal rocked them a little bit," he told nufc.co.uk. "From then to about 40 minutes, I thought we were excellent - much the better team and could maybe have had a couple more goals.
"2-0 is a dangerous lead, but we managed it well. Freddie (Woodman)'s made two saves, and they're two saves I'd expect him to make - the first one's just above his head, and the other one, he got it away from the goal well.
"We had some good situations in the second half and the final pass maybe just let us down, but overall I'm very pleased.
"Owen Bailey, as a young lad who's not really experienced at this level yet, did well for us, so there's always massive pluses. I think Liam Gibson was really good and Yasin, in the first half in particular, I thought was really good. He had a bit of end product, so there were a lot of good things for us."
A crowd of 508 watched the Tyne-Tees derby under the lights at St. James', as Boro opted to field first-teamers Grant Leadbitter and Carlos De Pena for the clash.But the youthful Magpies prevailed, and Beardsley said he was happy with how his side "managed" the contest.
"I thought we managed the game well, and in the end I think 2-0 was probably a fair reflection," he said.
"Any win's a good win, but in a local derby especially. We lost to them two years ago when we were in the same league - (Emmanuel) Ledesma scored early, and they sort of just hung on and managed the game. They had a few more experienced players that night.
"But fair play to the boys - it was a comfortable 2-0 in the end."
