Both sides came into the game short of form, resulting in a scrappy first half devoid of chances and quality at the Cardiff City Stadium.
However, the hosts seized the initiative after the break and took the lead through Peter Whittingham's excellent header from a fine cross by Craig Noone - starting in the Premier League for the first time.
West Brom saw strong appeals for a penalty turned down as it sought an equalizer, but remains with just one away win to its name all season - September's memorable triumph at Manchester United.
Cardiff made three changes from last week's defeat at Crystal Palace, including the recall of Peter Odemwingie against his former club, while West Brom reinstated Jonas Olsson and Shane Long to their side.
After Boaz Myhill tipped Whittingham's free-kick away, Gary Medel lashed an effort over the crossbar as the hosts settled into the game quickly, but the opening period was characterized by sloppy possession from both sides with neither goalkeeper fully tested.
The heavens opened during the halftime break, making conditions tricky, but Cardiff began the second period strongly and Odemwingie blasted over as West Brom dithered on the edge of its own box.
The visitors had a superb chance to score in the 56th minute as Morgan Amalfitano squared to Claudio Yacob, whose mis-hit fell kindly for McAuley, but the Northern Ireland defender was denied on the line by a combination of Medel and keeper David Marshall.
Cardiff then broke the deadlock on 65 minutes, Noone swinging a great ball in from the right and Whittingham directing his header beyond Myhill.
Both teams saw penalty appeals waved away by referee Howard Webb, with West Brom particularly aggrieved as Shane Long was bundled over in the penalty area by Ben Turner.
Substitutes Scott Sinclair - jeered onto the pitch as a former Swansea City player - and Saido Berahino combined well out wide with the latter's cross somehow evading colleagues in the box.
And West Brom threatened again soon after, McAuley heading across the face of goal, before Marshall rescued the result with a magnificent reaction save to keep out Long's firm header.
The win moves Cardiff four points clear of the relegation zone, and above West Brom - which has now lost four successive matches.
Follow GOAL.COM USA on Twitter