After a goalless first-half at Whitley Park, the young Magpies trailed shortly after the restart through Fenton Heard's deflected strike before Parkinson's equaliser, followed by Kyle Crossley's quick-fire brace, swiftly turned the contest in United's favour.
Despite Harry Whitwell's stoppage-time strike halving the deficit, Newcastle's youngsters recorded a valuable three points to enhance their qualification hopes for the top 16 spots in the division.
Parkinson, who made his Premier League debut for the Magpies' first-team away at AFC Bournemouth in November 2023, told nufc.co.uk: "Where we are at this point of the season, it's crunch time and we need to start winning games no matter how we get it over the line. We got three points tonight and coming from behind to win makes it even sweeter.
"I think we flipped a switch once we conceded. We knew we needed to get back into the game and had to change something. West Brom came with something completely different and we prepared for a high-pressing team with a back five but, instead, they had four and sat back, letting us play in front of them.
"It was just about adapting to the game but I thought we dealt with that very well."
Parkinson extended his goalscoring tally to six across all competitions at under-21 level, netting a third goal in his last four league starts for United's youngsters.
The 19-year-old forward, who signed his first professional contract with his boyhood club last summer, is determined to continue his contributions in front of goal during the latter stages of the 2023/24 campaign.
"I want to be scoring goals," the Durham-born teenager added. "I've got three in my last four league starts now so I'm pleased on a personal level.
"I've had a bit of a stop start season with the under-21s and getting a run of games so it's been really good for me lately. I really enjoy playing football no matter where I'm playing.
"Playing up front and scoring goals is what I want to do and, ultimately, I think that's what I'm starting to prove that I can do once I get a bit of consistency in my game.
"I'm buzzing for Kyle as well, coming off the bench and scoring twice to help us win the game."
Newcastle's second-string currently occupy 21st place in the Premier League 2, four points adrift of the top 16 spots, and Parkinson is keen for a bright flourish in the young Magpies' final four league fixtures.
"We want to be in the top 16 and don't want our season to be cut short," he added. "We're all itching to play games as it's been a strange season with games being called off left, right and centre so to get a run of games is really important for the group.
"We want to get into the play-off spots and push to try and win the whole thing."