The Spireites hit the woodwork through Adi Yussuf and had a goal ruled out in the first-half at the Technique Stadium.
But goalkeeper James Montgomery ensured they claimed at least a point with some good saves after the break.
The draw leaves the Blues in the last play-off spot in seventh with two games remaining against Dagenham and Redbridge and Halifax.
Here are Liam Norcliffe’s player ratings from the game...
1. James Montgomery 9
Chesterfield could have won this game but they could easily have lost it had it not been for some good saves by Montgomery, particularly in the second-half. Photo: Rachel Atkins
2. Josef Yarney 6
Had a goal ruled out in the first-half after Yussuf was penalised for handball. He could have been better in possession and Wealdstone's Lewis got in behind in him a couple of times with his pace, one which almost won the game for the visitors late on. Photo: jason chadwick
3. Will Evans 7
A fairly solid performance considering it was his first start in two months. Made a crucial block in the second-half from Hughes in the box. Photo: Dean Atkins
4. Laurence Maguire 6
Not really troubled too much defensively. Could have probably done better with his crossing at times. Photo: jason chadwick