Neither side had won in their previous five games, but Whittingham's fine finish from a Craig Noone cross in the 65th minute gave the hosts a merited three points and opened up a little breathing space to the bottom three for Malky Mackay's side.
It was Albion's fourth straight defeat and manager Steve Clarke will be as concerned as fellow Scot Mackay was relieved by this result.
The Baggies were ineffectual and such a poor performance against opponents who are far from on the best of form themselves gives Clarke plenty to ponder.
Both these teams had won just one of their last nine games, while Cardiff had gone three games without scoring.
It prompted a lively start from the hosts, with Odemwingie working Boaz Myhill with a sharp free-kick.
Winger Noone also featured prominently, testing Liam Ridgewell and turning in a threatening cross which Jonas Olsson turned behind with Campbell lurking.
The best early chance fell to Steven Caulker, Turner flicked on Whittingham's corner but the England centre-half put his shot wide with Myhill stranded out of position.
But, after Campbell just failed to get on the end of a driven Odemwingie cross, the first half fizzled out.
The visitors created very little and Cardiff's only real alarm came when Andrew Taylor inadvertently diverted a pass across goal, but David Marshall made an easy save.
Cardiff pressed again at the start of the second half, but it was West Brom who carved out the clearest chance.
Morgan Amalfitano pulled back to Claudio Yacob but the Argentinian scuffed his shot to McAuley who made a better fist of hitting the target, only for Gary Medel to block on the line, with Marshall also in attendance.
Cardiff hit back and took the lead. The excellent Noone delivered a pinpoint cross which Whittingham headed wide of Myhill's despairing dive into the bottom corner.
Caulker came close to doubling the lead from a Whittingham corner a few moments later, only for Odemwingie to get in the way and flick the ball away from goal.
The game had suddenly sprang to life and West Brom had a decent penalty shout turned down by referee Howard Webb.
Shane Long appeared to be bundled over by Turner as he turned in the box, but the Republic of Ireland striker was waved to his feet.
Jordon Mutch then fired over after cleverly making room for himself on the edge of the box.
Clarke sent on Saido Berahino and Scott Sinclair as his side launched a late bid for an equaliser.
But their final chance came and went when a Long header was brilliantly saved by a full-stretch Marshall.
- Sports & Recreation
- Malky Mackay
- Fraizer Campbell
- Steve Clarke
- Peter Odemwingie
- Boaz Myhill