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.
The signs were there early on, as Berahino and Ideye linked up to win the corner that created the first opening in the 12th minute.
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.
The visitors grew into the game after that and passed the ball about at will, unchallenged by West Brom.
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.
West Brom got their reward for that positive approach in the 75th minute when more purposeful running from the front two put Swansea on the back foot and created space in the box.
Ideye and Berahino then exchanged passes before the latter curled into the top corner with a first-time right-footed shot from 15 yards - his 10th league goal of the season.
Swansea rarely troubled West Brom after that second goal as the hosts cruised to an important victory.
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