The Clarets had drawn their previous three games 0-0 but their defence was put under pressure by the Hawthorns hosts from the first whistle and was breached by Craig Dawson on the half-hour mark before Berahino netted twice either side of the interval.
The England Under-21 forward now has five goals for the season, with the Clarets having netted just once between them.
They have not scored in eight hours and 46 minutes in the Premier League and already look destined for a long fight against the drop.
Graham Dorrans wrapped up the win – Albion’s third in a row in all competitions – with a strike from inside the area in the 90th minute.
The victory lifts Alan Irvine’s Baggies to 10th in the table after six games, while Burnley sink to the bottom on goal difference.
Irvine named an unchanged Albion side from their 1-0 win at Tottenham last week, their first victory of the season under their new head coach.
Berahino started after coming off the bench to score the late winner in Wednesday’s 3-2 Capital Cup win over Hull.
Victor Anichebe and Brown Ideye were ruled out with hernia and ankle injuries respectively.
Burnley recalled Ross Wallace, Michael Kightly and Steven Reid, who left the Baggies in the summer after a four-year stay at The Hawthorns.
David Jones (thigh) and Dean Marney (hamstring) failed to recover from their injuries after starting last week’s 0-0 draw with Sunderland.
Burnley had not scored in the league in 436 minutes coming into the game and their lack of quality was evident from the start.
Kightly shot over for the Clarets before Chris Brunt’s drive deflected off Michael Duff and dropped inches wide after 15 minutes.
Berahino drilled across goal as the hosts took charge and tried to add to their own measly goal tally of just one in the last 376 minutes of league football before the game.
And the opener came on 30 minutes to reward the Baggies for their more inventive play when Dawson headed in Brunt’s deep corner from five yards.
It was bitter for Burnley, who had three bids rejected for the defender – who also handed in a transfer request – in the summer.
Brunt then volleyed over four minutes before the break and Tom Heaton superbly turned Dorrans’ fierce 25-yard drive behind.
Albion were hunting a second and it came in first-half injury time as Berahino netted his fourth of the season, nodding in from a yard out after Dorrans flicked on James Morrison’s corner.
Burnley offered little resistance with the Baggies in total control, and they hauled off Wallace and Reid for Nathaniel Chalobah and Ashley Barnes at half-time.
Chalobah’s first action was to pick up a yellow card for a foul on Dorrans and the changes made little difference.
The composed hosts continued to press as Craig Gardner’s deflected effort arrowed wide and Ben Mee blocked Stephane Sessegnon’s volley.
Albion confirmed their dominance with a third on 56 minutes when Dorrans’ pass split the Burnley defence for Berahino to drill low into the corner from 15 yards.
There was no way back for the visitors, although Ben Foster did well to keep out Lukas Jutkiewicz’s header on 66 minutes.
Barnes ballooned over three minutes later as the Baggies switched off but there was little further danger.
And it was left to Dorrans to add the gloss with a minute left when he swept in from 14 yards after substitute Cristian Gamboa’s cross from the right.
Albion’s next assignment is away to Liverpool next Saturday, when Burnley travel to Leicester.