Philliskirk struck with his third goal in two games - and his seventh of the season - before substitute Adam Rooney made the game safe to set up a second-round tie at home against Mansfield.
Wolves' leading scorer Leigh Griffiths grabbed a stoppage-time consolation but it was of little consequence after a low-key display by Kenny Jackett's side.
Philliskirk's 21st-minute opener owed a lot to an error by the normally reliable goalkeeper Carl Ikeme.
Ikeme had earlier denied Philliskirk with a smart save but he gifted Oldham their opening goal.
Ikeme appeared to have held on to a low free-kick from Johnson Clarke-Harris but let the ball squirm from his grasp and the alert Philliskirk was on hand to stab his shot over the line from two yards.
Philliskirk should have doubled Oldham's advantage at the start of the second-half only for Ikeme to make a spectacular save with his legs before he drilled another shot off the foot of the post.
But Rooney sealed the victory 60 seconds later in the 72nd minute - beating Ikeme with a low drive after a pass form Sidney Schmeltz.
Griffiths, moments after hitting a post, took his tally for the season to 11 after a cross from Zeli Ismail but Oldham fully deserved their win in front of a crowd of just 4,226 - the lowest at Molineux for more then 20 years.