Extra time isn't is the competition rule book with the game going straight to penalties after 90 minutes.
And it was the same combination which brought about their first-half goal as David Mellor played a ball to Philliskirk who produced a great turn before seeing his shot superbly saved by keeper Tommy Lee.
Jonson Clarke-Harris (pictured) made a weaving run before shooting just wide of the far upright.
Sam Hird was booked for a foul on Clarke-Harris who picked himself up and walloped a 35-yard free kick which forced a decent diving save from Lee.
Lee had to be at his best again to beat away a shot from Jonathan Grounds which followed a terrific run from defence.
Latics made their first substitution with 10 minutes left as Michael Petrasso made way for Adam Rooney as Philliskirk moved wide right.
James Wesolowski was replaced by Anton Rodgers in the 86th minute, Latics' second change.
Rooney burst clear on the right with one minute left but was thwarted by Lee.
Full-time: Latics 1, Chesterfield 1.