Berahino scored shortly before half time after a bright opening period from the visitors, who had two superb chances missed by midfielder John Oster.
Victor Anichebe added a second in first-half stoppage time, before Berahino scored a wonderful strike moments after the restart, then Chris Brunt added another before Berahino sealed his hat-trick, with James Morrison tapping in as Berahino scored a stunning fourth individual goal to cap an excellent performance.
The visitors started brightest and had a good chance early on as Oster fired a 20-yard free kick straight at Boaz Myhill.
Michael Rankine then had a close-range volley saved by the goalkeeper, while Matty Pattison drilled a low shot at the Baggies shot-stopper.
Pulis started in the stands but quickly moved down to the touchline, barking orders to his players after a bright start from the non-league outfit.
Gateshead’s pressure continued and Oster had another glorious chance, firing over after good work from Pattison on the right.
But it was the hosts who finally broke the deadlock just a few minutes before the break as they won a free kick on the right-hand side. Chris Brunt fired it in low and after a goalmouth scramble Berahino fired a perfect volley into the roof of the net.
It was soon 2-0 as Anichebe ran on to a pass into the box, holding off his man before spinning and shooting across the goalkeeper and into the far corner.
The hosts blew their non-league opposition away immediately after the break, Berahino adding his second of the afternoon as he picked the ball up in space and moved forward before curling a wonderful strike into the top corner.
The striker then sealed his hat-trick after good work from Chris Baird, and he swept home the cross to make it 4-0, before Chris Brunt added a fifth moments later, rounding the goalkeeper after meeting Giorgios Samaras’ fine ball through.
The latter stages were played at a much slower pace as the visitors ran out of steam and Pulis’ side conserved energy, but they still had time to add a sixth as Silvestre Varela fires a low ball across the six-yard box and Morrison was there to tap in at the far post.
Berahino wasn’t done, however, and he netted his fourth of the match in stoppage time as he cut in from the left-hand side and curled a wonderful shot into the far corner to seal an emphatic win.