West Brom's record signing, Ideye, appeared to be on the verge of leaving the club last month but underlined his value with a rare moment of quality to make breakthrough on the hour mark at The Hawthorns.
His strike partner Berahino, recalled after being dropped for Sunday's draw at Burnley, put the result beyond doubt with a well-taken second 15 minutes from time.
Tony Pulis will have been pleased to see his front two combine so well, teeing each other up for their goals, which saw West Brom climb to 14th.
Meanwhile, Garry Monk's men offered little in response as their mid-table malaise continues.
Craig Dawson met James Morrison's set-piece with a flicked header that forced a fine save from Lukasz Fabianski, which the goalkeeper followed with a brave dive at the feet of Ideye.
Despite promising early possession, Swansea offered little going forward until the 26th minute when Jefferson Montero skipped past Dawson on the left and teed up Bafetimbi Gomis, but Gareth McAuley did enough to put him off.
That allowed Jonjo Shelvey space to try his luck from 25 yards after 33 minutes but while his effort beat Ben Foster, it flew just wide of the post.
Gomis called Foster into action for the first time three minutes later when a loose ball dropped to him from a corner, but the Frenchman volleyed straight at the goalkeeper.
The second half followed a similar pattern in the early stages, with neither side capable of really taking control.
But when Berahino broke forward and played a ball into his strike partner Ideye after 60 minutes, the deadlock was broken. Ideye was initially held up by an Ashley Williams challenge inside the box, but the ball fell kindly for the striker to sweep home from 12 yards.
It was his second goal in four days following his effort against Burnley - having scored just once in the Premier League in the first half of the season - but he was far from done. The powerful striker continued to drive his team forward, roared on by Pulis as new captain Darren Fletcher controlled the midfield.
