A comprehensive second-half performance by the home side boosted their play-off chances, with David Dowson and Jamie Ward both scoring twice in what was a rout.
The disturbing thing for Town was the total contrast between their first-half display and what became a mismatch after the interval.
Paul Simpson's team were unrecognisable from the side that had matched Chesterfield and they still need at least one more victory to be confident of avoiding relegation.
If they play as poorly as they did in the second half, it is difficult to see where the points will come from, although they will not encounter many teams with strikers as confident as Dowson and Ward.
Dowson opened the scoring two minutes after the interval when Shrewsbury backed off him and he accepted the invitation with a low drive from just inside the box that left Glyn Garner with no chance.
The goalkeeper was then beaten three minutes later by a stunning strike from Ward, whose righ- foot volley from 20 yards whistled into the top right corner.
Simpson responded by making two substitutions, but his team fell further behind when Ward was allowed to run clear on to a long ball and score his 11th goal of the season with a low shot.
The game was now finished as a contest and it was a question of how many Chesterfield might score against a team that was looking demoralised.
But to Shrewsbury's credit they had responded with a spectacular goal of their own nine minutes from the end when Kevin McIntyre sent a 25-yard shot past Barry Roche.
It was the midfielder's first goal since joining Shrewsbury in January, but the final word went to Chesterfield who scored again in stoppage time.
This time it was Dowson who struck after a clever one-two with substitute Bruce Dyer, to leave Shrewsbury with only one win in their last 19 matches.