A Grant Holt penalty had given the Shrews the lead, but Chester hit back just before the break through Paul McManus.
Shrewsbury had started the game on the front foot and should have taken the lead after only two minutes when an in-swinging free-kick from Ben Davies was met by a diving header from Holt, but the striker's effort was wide of the target.
The home side appeared to have weathered the early storm and saw Kevin Ellison curl a free-kick against the post and Mark Hughes head an effort wide.
But the Shrews took the lead on 29 minutes when they were awarded a controversial penalty.
Davies went down in the box under a challenge from James Vaughan and Holt made no mistake with the spot-kick sending John Danby the wrong way.
Chester levelled matters on 43 minutes when Ryan Lowe's right-wing cross was deftly touched in by McManus off the post.
Ellison went close with a header from Lowe's corner early in the second half and, at the other end, Kevin Roberts produced a superb block to deny Dave Hibbert's goalbound shot.
On 69 minutes, Ellison had a great chance when the ball broke to him on the penalty spot, but the chance fell on his weaker right foot and he dragged his shot wide of the post.
The Shrews then hit the post twice in the space of a minute.
Firstly, substitute Chris Humphrey connected with a volley which came back off the post, then in the next attack Hibbert out-stripped the Chester defence but saw his effort hit the outside of the post as the game ended all square.