Beattie made it six goals in 10 games for Stoke since his £3.5million January switch from Sheffield United as City finally picked up their first away league win of the season - and completed a seasonal double against Albion in the process.
Beattie struck at the start of the second half to seal the win that had been set up when Ricardo Fuller helped himself to his eighth goal of the season after just two minutes.
Albion, who are now 11 points adrift of Stoke, had a hand in their own downfall as they made errors for both goals as their dismal run against their bogey side continued.
They have now beaten Stoke just once in the last 27 league meetings and they never really looked capable of easing that dismal statistic once Fuller had struck.
They remain rooted to the bottom of the table and hopes of pulling off another great escape are fading fast as they have now failed to win any of their last nine league games and are cut adrift of safety with just seven games remaining.
In contrast, Stoke are within touching distance of securing another top-flight season after back-to-back wins and a run of just one defeat in their last six games.
Fuller's early strike was a personal disaster for Albion central defender Shelton Martis and goalkeeper Scott Carson.
Martis totally lost the flight of the ball when Stoke left-back Danny Higginbotham played what appeared to be a hopeful long punt up field.
But Martis failed to deal with the ball and then he saw Fuller muscle his way past him and surge towards the edge of the area.
Fuller then let fly with a right-foot drive that didn't seem to carry much pace.
Carson even managed to get to his hands to the ball only to see it slide through his fingers.
While Carson will feel he should have done better with Fuller's shot, he did go some way to making amends three minutes later when he made what was markedly a more difficult save to push a Glenn Whelan free-kick around the post.
Albion struggled to get to grips with the game after that nightmare start and although James Morrison tested Thomas Sorensen from close range, it was Stoke who carried by far the greater threat.
They should really have doubled their advantage after 26 minutes when Fuller fed Whelan, whose neat through ball fell neatly into the path of Matthew Etherington.
He only had Carson to beat from the right hand edge of the area however the angle was acute and the former West Ham winger pulled his shot across the face of goal.
But Stoke did not have to wait too much longer to deliver a knockout blow to Albion.
Once again, Albion were guilty of pushing the self-destruct button when Fuller lifted the ball into the penalty area.
Central defender Jonas Olsson and right-back Gianni Zuiverloon both tried to clear Fuller's cross but all they did was get in each other's way.
That let the ball bounce into the path of Beattie who made no mistake with a rising volley from 12 yards.
Albion's dismal day was then perfectly summed up in the closing stages when Chris Brunt crashed a 35-yard drive off the bar and substitute Roman Bednar saw his effort disallowed for offside.