Chester have now taken only 10 points out of the last 72 and are still not safe from relegation, although they came closest to scoring when Paul McManus hit the post after eight minutes.
Shrewsbury, with only 14 points out of the last 72, themselves rarely threatened. Chris Humphrey was a danger on the right wing and had one stinging left-foot shot tipped round the post by John Danby.
The Shrews made three changes from their defeat at Mansfield last Saturday but lacked punch even after a late double substitution.
Guy Madjo was agonisingly close to getting a touch as the ball rolled along the line and Ben Davies, off-colour against his old club, had a late shot which was deflected but Danby gathered easily.