Both teams had players missing and Oldham appeared to be on course for all three points at Saltergate when Paul Warne gave them the lead two minutes after the break.
But Allison showed his power in the air with a typical close range header and the game could have gone either way in the final ten minutes.
In the end a draw was probably about right, although Chesterfield keeper Barry Roach had to make two outstanding second half saves to keep his team in the game.
The first half had been virtually devoid of any incident as the ball was needlessly given away in a scrappy and disjointed periods of playing.
But Oldham took the lead with the first moment of real quality in the match when former Chesterfield striker Luke Beckett set-up Warne who finished well with his left foot from 15 yards.
Oldham might have sealed the points eight minutes later when midfielder Richie Wellens surged through the middle and drove in a low shot which Roach saved to his right.
The importance of that was underlined when substitute Adam Smith produced a brilliant cross to the back post in the 68th minute and Allison powered a header into the roof of the net.
Oldham almost regained the lead in the 78th minute when Liddell unleashed a fierce shot that Roach parried and Beckett put the rebound over the bar.
Chesterfield also had chances with Paul Hall going very close with a late header, while Colin Larkin also had a shot charged down.