The striker, who scored 18 goals last season, fired in an acrobatic effort deep into stoppage time to make it four unbeaten for the Minstermen.
The Spireites opened the scoring in the 35th minute as summer signing Sam Hird tapped home for his first Chesterfield goal.
Richard O'Donnell would be picking the ball out of the net at the other end seconds later as Michael Coulson continued his impressive start in a York shirt, latching onto Walker's pass before producing a neat finish.
The visitors were behind again a minute later as Craig Westcarr raced away before placing the ball beyond Michael Ingham's reach.
With the final whistle beckoning, Walker's touch of quality earned York a point.