Longstaff has now netted seven times in his last eight appearances, sitting comfortably as the young Magpies' leading marksman this term.
He broke the deadlock midway through the first-half at Little Benton, rounding 'keeper Ryan Catterick before slotting into an empty net.
After the visitors restored parity through winger Rhys Oates, Longstaff gave Beardsley's charges a commanding lead with two quick-fire goals after the break.
Elias Sorensen added a fourth after 81 minutes, before Longstaff unselfishly teed up the young Dane for another late on.
It capped off an impressive all-round display from the 18-year-old, though Beardsley believes he can still fine-tune his finishing further.
"Sean is on a good run at the moment, and that will give him confidence," he told nufc.co.uk. "He has a good energy about him, he can run beyond people, and he is always in the box.
"The more he scores, the better he is going to be. He has eight for the season, but he maybe could have had 12 or 13. I'm probably being a little harsh there, but that's the reality. He maybe should have had two or three at Fulham on Monday night.
"The pleasing thing for me - being the type of player that I was - was that he was prepared to pass to Elias late on when he could have scored a fourth himself. Fair play to him for that."
Beardsley rested Dan Barlaser and Jamie Holmes for Pools' visit, with Dan Ward, Adam Wilson and Stuart Findlay all coming into the side.
With Newcastle set to face another North East outfit, Middlesbrough, at St. James' Park on Monday, Beardsley was pleased to see his selection policy pay dividends.
"It's a game we wanted to win, but - without being disrespectful - it was a game we thought we could win even though we didn't have our strongest team," he said.
"The first-half display was decent. They only had one shot and they scored, which was frustrating in that sense. While it's 1-1, you're never comfortable, but we should have been more comfortable than we were.
"In the second-half, we managed the game well, played some lovely football and ran out comfortable winners."
