After last weekend's surprise success at Tottenham and a League Cup victory over Hull City, Alan Irvine's side maintained recent momentum on Sunday thanks to goals from close-season Burnley transfer target Craig Dawson, Berahino, who was also on target twice against Sunderland on the opening day of the season, and Graham Dorrans.
That Albion's first two goals came as a result of sloppy Burnley defending from corners will give manager Sean Dyche plenty to ponder, especially as the Lancashire club travelled to The Hawthorns on the back of three straight clean sheets.
Albion played with more freedom in the second half. Berahino's speed and clinical finishing soon put the game beyond doubt with his side's third after 56 minutes, with Dorrans also on target late on.
On the evidence of Sunday's game, Dyche has a big job on his hands to keep his side in the top flight, while West Brom celebrated a second league win of the campaign.
West Brom's starting XI was unchanged from last weekend's win at Tottenham, while Burnley, who were again without injured trio Danny Ings, Sam Vokes and Matt Taylor, brought in former Albion player Steven Reid in a holding-midfield role, Ross Wallace and Michael Kightly to replace Marvin Sordell, David Jones and Dean Marney.
The visitors had an early penalty appeal turned down when George Boyd's cross struck Andre Wisdom on the shoulder, but otherwise offered little in attack and tried to focus on keeping it tight at the back.
Their resistance was broken after half an hour, though, when Dawson climbed high above Jason Shackell at the back post to head in a Chris Brunt corner for his first Albion goal since joining from Rochdale four years ago.
Tom Heaton had to be alert to stop Albion from going further in front when tipping a long-range Dorrans strike over the bar.
But a second goal for the home side did arrive in first-half stoppage time when Berahino nodded in from close range after Dorrans had flicked on a James Morrison corner.
Dyche reacted at the interval by bringing on Ashley Barnes and Nathaniel Chalobah for Reid and Wallace.
Chalobah's first taste of action earned him a booking for a lunge on Craig Gardner, who soon after went close with a long-range strike, while Stephane Sessegnon's volley was well blocked by Ben Mee as the hosts continued to boss proceedings.
And good work from Brunt and Dorrans then put Berahino clean through on goal and he fired low past Heaton on 56 minutes to make it three.
West Brom goalkeeper Ben Foster was forced to make a smart save after Lukas Jutkiewicz rose above Dawson and headed powerfully on target and Barnes should have done better when set up by third substitute Sordell.
Dorrans made it 4-0 after 90 minutes following good work down the right by substitute Cristian Gamboa, neatly tucking his low shot past the outstretched Heaton to send Burnley bottom on goal difference.
