In a game which only came to life after the break, half-time substitute Richard Walker secured the points for Paul Simpson's men with the decisive goal just before the hour.
Despite having numerous opportunities to make the match safe, Shrewsbury were unable to manage a second goal to ensure the points, although their task was made easier with 11 minutes left when Chester's Jay Harris was sent off for a bad challenge on Shrews winger Chris Humphrey.
The home side were denied more goals by some poor finishing - and also an outstanding display from Chester keeper John Danby, who distinguished himself with a series of fine saves, including two from Shrewsbury top scorer Grant Holt in the space of a minute in the second half, that were of the very highest order.
Without a win in their last nine games and only one point from a possible 18, Chester managed to keep Shrewsbury at bay during a lack-lustre first half when the home side struggled to find any rhythm.
But they were roused into action early in the second half when Chester - with their first significant attack of the game - almost snatched the lead.
The hard-working Kevin Ellison cut in from the left and, despite his curling shot beating Shrewsbury keeper Luke Daniels, it thumped against a post and rebounded to safety.
In the 57th minute, however, it was Shrewsbury who finally broke the deadlock when Humphrey burst into the penalty area and crossed to the far post where Walker was on hand to tap in his seventh goal of the season.
Shrewsbury then launched a fierce onslaught but, due to some heroics from Danby combined with a lack of composure in front of goal, they could not extend their lead, although the dismissal of Harris put paid to any hopes the visitors had of salvaging a point.