Highly-rated striker Berahino, who has been linked with a move away from The Hawthorns, took his tally to 13 goals for the season with four clinical finishes as Albion blew non-League Gateshead away in Saturday's third-round tie.
It was not all plain sailing for the Premier League strugglers, as they were second best for much of the first half but goals from Berahino and the recalled Victor Anichebe just before the break stunned the Conference National side.
New head coach Pulis, who was appointed as Alan Irvine's successor on New Year's Day and was given a rapturous reception from Albion fans, planned to watch the game from the stands but he was soon his usual animated self on the touchline as his side were lacklustre in the opening period.
Ruthless Albion moved up a gear in the second half and taught Gateshead a lesson as they struck three times in the first 10 minutes after the interval to end any hopes of a fightback.
Berahino was on target a minute after the break with a fine strike from outside the penalty area before adding a further two goals in an outstanding display of finishing either side of strikes from Chris Brunt and James Morrison as Gateshead wilted.
Gateshead looked very much at home as they started with confidence and Michael Rankine had a chance to put them in front when Albion failed to deal with a corner and the striker's attempt from close range was straight at Boaz Myhill 12 minutes in.
A disgruntled Pulis was clearly not impressed with what he saw as he came down from the stands to bellow out orders from the touchline after only 15 minutes.
Pulis' words failed to spark Albion into life and John Oster spurned a good opportunity to open the scoring when Matty Pattison cut the ball back for the former Everton man, but he blazed over the crossbar when unmarked in the penalty area.
The underdogs were made to pay for a lack of clinical finishing when Berahino struck three minutes ahead of half-time with a composed right-foot finish after Gateshead failed to deal with a Brunt free-kick.
Anichebe then dealt a body blow to Gateshead when he took a Berahino pass and rolled his marker before rifling into the roof of the net in first-half stoppage time.
There was more misery for Gary Mills' men less than a minute into the second half, when Berahino showed his class with a sublime measured right-foot strike inside the right-hand post to put Albion out of sight.
Anichebe almost doubled his tally with a low strike which forced a fine save from Adam Bartlett, but the Gateshead goalkeeper was unable to prevent Berahino from completing his hat-trick after 53 minutes.
The striker found the far corner of the net with a clinical first-time finish from 10 yards out after Chris Baird picked him out and Brunt added a fifth goal two minutes later as demoralised Gateshead crumbled.
Northern Ireland midfielder Brunt raced clear and rounded Bartlett before tucking the ball into the empty net after substitute Georgios Samaras picked him out.
Morrison added a sixth goal when he tapped home at the far post 11 minutes from time and Berahino had the final say with another stunning right-foot finish after 90 minutes as Gateshead failed to recover from Albion's blitz either side of half-time and bowed out with a heavy defeat.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
