The young Magpies led inside four minutes at the Impact Arena through Anderson's penalty after Joe White was bundled over inside the penalty area before Forest goalkeeper Nicky Hogarth received a red card after handling the ball outside the box.
Anderson's clinical finish doubled his and United's tally shortly after the restart before the 19-year-old forward, who made his Magpies first-team debut in January, completed his hat-trick after pouncing on a defensive error before rifling the ball home.
The North Shields-born teenager, who recently received an international call-up for Scotland at under-21 level, was thrilled to take his count to seven goals so far this term as he sets his sights on breaking into Newcastle's first-team.
"I'm buzzing," Anderson told nufc.co.uk. "I haven't played in three or four weeks and to score a hat-trick to get my goal tally up is quite important to me.
"In the short-term, I'm trying to impress the manager as much as I can, show what I've got and see if he notices.
"I thought we started the game really well and the intensity was high. They got a man sent off within the first ten minutes but we played like we have been in training. I think to come down here and pass them off the park has been a successful day for us."
United's second-string have moved within one point of the Division Two play-off spots and Anderson, who made his Premier League debut for his boyhood club in January, is determined for Newcastle's youngsters to build on their impressive victory against Forest.
He added: "Scoring the first goal gave us a bit of time to play and we were a bit more confident with the ball, building it up from the back. We could have been a bit more faster with the ball and killed them a bit more but it definitely gave us that boost.
"The red card was good for us and we were able to capitalise on it, making sure that we made them suffer from it, which was good.
"It's important to keep your standards high and as a captain myself, I was trying to tell the lads to maintain the high standards on the pitch and Elliott (Dickman) told us that at half-time.
"Getting the second gave us another boost, more breathing space, and showed that we could go on to get more. We set out to get a lot of goals and you could see forward runs still being made in the 80th minute.
"We were unlucky to concede late on in the game but I think we managed the game well and got three points.
"We're back to winning ways (ending a run of five winless matches) which builds the lads' confidence and shows that we can come away to places and turn teams over. We need to start building on from this and try to get more wins in the next two weeks or so."