The Baggies centre-back was given his marching orders in the 76th minute when he was questionably sent from the pitch for a late tackle on FC Sion winger Demetris Christofi.
Huddersfield Town's Martin Paterson had a great chance to open the scoring in the 12th minute when he met Nial McGinn's cross with his head but Cyprus keeper Antonis Giorgallidis was able to keep it out.
Cyprus' best chance in the opening half came late when Efstathios Aloneftis played in Christofi only to see Northern Ireland gloveman Alan Mannus palm it over the bar.
Michael O'Neill's side were seeking just a second win in their past 20 outings but were forced to hold on when McAuley saw red with 15 minutes remaining.
Veteran keeper Roy Carroll, who had earlier replaced Mannus, denied the home side a last-gasp victory when he denied Andreas Makris from close range.
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