After a goalless first half in which Kevin Ellison had struck the woodwork, the game came to life with four goals in an 11-minute spell.
The deadlock was broken on 62 minutes with a moment of individual brilliance from Richie Partridge. The winger advanced with purpose and then picked his spot with a measured curling shot into the back of the net from 20 yards.
The visitors levelled matters on 69 minutes through former Chester player Darren Moss. Dave Hunt delivered a free-kick from the right and Moss arrived unmarked to head the ball home from close range.
That parity was short-lived as Chester hit back with two goals in as many minutes. First on 72 minutes, a mix-up between Neil Ashton and Kelvin Langmead allowed John Murphy in and he made no mistake slotting the ball past the keeper.
A minute later the ball was in the back of the net again as the ball was headed forward by Tony Dinning and sub Simon Yeo hit a stunning first-time volley that gave the keeper no chance.
There had been little sign in the first half of the goals that were to come in the second period. The nearest to a goal had been on five minutes when Shrews keeper Glynn Garner had a let-off when his kick was charged down by Murphy. The Chester striker squared the ball to Ellison whose shot from six yards out struck the woodwork.
Shrews captain Stewart Drummond had several good chances and saw a header cleared of the by Dinning. He also went perilously close to scoring just before half-time, but got only the faintest of touches on the ball and his header flew wide.
Keeper Garner had clawed away a looping header from Murphy on the hour mark which had been heading for the top corner and then the game really sprung to life as the goals came in quick succession and Chester gained an impressive win.