Allison out-jumped United's defence 17 minutes from time to cancel out Jamie Gosling's earlier strike for the Gulls.
Leroy Rosenior's man came into the game having lost their last three but they gave themselves a great chance of ending that dismal run with the opening goal on 48 minutes.
Alex Russell chipped a superb ball over the Spireites defence and Gosling fired into and empty net after Carl Muggleton blocked Tony Bedeau.
Moments later Muggleton brilliantly kept out Leon Constantine's snapshot form 12 yards, but from then on the home side took control.
Aaron Downes came close with a header before Allison, who came on after 66 minutes, nodded fellow substitute Adam Smith's cross into the bottom corner.
Caleb Folan and Sammy Clingan then went close as Chesterfield pushed in search of the winner.
But the Gulls held on for a well-deserved point.