Philliskirk's 12th strike of the season settled a closely-fought contest and earned the Latics their first victory in six attempts.
They went ahead in the 18th minute as Korey Smith found Philliskirk, who turned sharply before drilling his shot inside the post from 12 yards.
The home side could have gained more reward for their dominant first-half display, but David Worrall fired a shot inches off target before Crawley goalkeeper Paul Jones saved with his feet from Jonson Clarke-Harris.
Crawley carved out their first opening after 56 minutes when Billy Clarke forced a good save from Oldham keeper Paul Rachubka, diving full-length to his left.
Jamie Proctor then headed straight at Rachubka, but Oldham wasted a chance as Clarke-Harris finished tamely from 14 yards.
With the pitch cutting up badly due to torrential rain, defensive errors crept in and Mike Jones almost levelled for the visitors.
But Oldham's Charlie MacDonald was denied by Jones and Crawley slipped to only their second defeat in 11 games.