Goals from Liam Mandeville and Kabongo Tshimanga put the hosts in a commanding position at the break.
But Matty Kosylo struck with six minutes remaining and then substitute A-Jay Leitch-Smith hit an equaliser in stoppage time.
The draw means Town are unbeaten in their last 10 matches and are one point clear at the top.
Here are Liam Norcliffe’s player ratings from the game at the Technique Stadium last night...
1. Scott Loach 6
He was on course for his 10th clean sheet of the season until the two late goals, which he probably could not have done much about. A mix-up between him and Grimes led to Altrincham being awarded an indirect free-kick inside Chesterfield's box in the first-half but he made himself big and did brilliantly to parry it wide. His kicking was more assured. Photo: Tina Jenner
2. Tyrone Williams 6
Steady enough and battled hard throughout. Still settling into his new surroundings but had acquited himself well so far. Looked like the late equaliser deflected in off him. Photo: Tina Jenner
3. Jamie Grimes 7
Made one key interception at 1-0. He sold Loach short with a back-pass which resulted in an indirect free-kick but thankfully they got away with that in the end. Assisted the second goal when he knocked down Mandeville's corner for Tshimanga to turn in. He won a number of other headers at each end. Photo: Tina Jenner
4. Luke Croll 6
He was decent enough. He was a threat in Altrincham's box from corners. Ended the night with an injury but carried on. He will be assessed. Photo: Tina Jenner