Town boss Gary Peters, who has set his side a target of 50 points this season, saw his side pick-up three more in splendid fashion to move ever further away from the lower reaches of League Two.
First-half goals from Jamie Tolley and revitalised striker Luke Rodgers saw the home side establish a comfortable half-time lead - before a Jake Sedgemore penalty and strikes from Ryan Lowe and Kelvin Langmead ensured the Shrews recorded their biggest win of the season and made it 14 goals in their last three home matches.
Although Chester started brightly, Ian Rush's men created few clear-cut openings from their greater share of possession and went behind in the 28th minute when Tolley bundled home a cross from Rodgers at the near post.
From provider Rodgers then put himself on the scoresheet, netting with a low drive from 20 yards four minutes before half-time - scoring in successive games after breaking a four-month duck against Kidderminster last Saturday.
Twelve minutes into the second half things went from bad to worse for Chester as they conceded a penalty and were reduced to ten men after defender George Elokobi was ordered off for upending Rodgers in the box.
Sedgemore slotted home the resulting spot-kick to put the issue beyond doubt and on 65 minutes Lowe celebrated his return to the starting line-up with a superb curling right-foot shot from 20 yards.
The best, however, was saved until last - in the 78th minute with a move started by a throw from goalkeeper Scott Howie, Shrewsbury swept down field with the ball finally arriving with Lowe.
He crossed into the box where Langmead rammed the ball home from eight yards to complete a memorable passage of play and a fine afternoon for the Gay Meadow outfit.