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 they sought an equaliser, but remain with just one away win to their 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 characterised by sloppy possession from both sides with neither goalkeeper fully tested.
Steven Caulker slashed wide from close range after Olsson failed to deal with a corner, while the former Tottenham defender had to be alert to deny Gareth McAuley from Chris Brunt's swirling set-piece.
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.
