The visitors had opened the scoring on 14 minutes. A defence-splitting pass from Leam Richardson found Aswad Thomas and the debutant made no mistake bringing the ball down with one touch and then instantly firing a precision shot past John Danby.
Accrington's lead was short-lived as Chester drew level six minutes later with a goal straight off the training ground.
Kevin Sandwith delivered a free-kick to the back post where John Murphy nodded the ball across the face of goal for captain Paul Butler to head home from close range.
The home side went ahead on 34 minutes after good work by Mark Hughes who got to the by-line and rolled the ball to Murphy whose shot looped off keeper Ian Dunbavin and crossed the goal-line.
Chester were on top and defender James Vaughan tried his luck with a 30-yard shot that whistled past the post. On the hour mark the on-loan Craig Lindfield had the ball in the net but was adjudged offside.
Accrington went close on 61 minutes when goalscorer Thomas forced Danby to make a reflex save when he powered a header goalwards from Shaun Whalley's corner.
Chester did not heed the warning when Thomas levelled matters, following the ball in after Danby could only parry Craney's initial shot.
Nine minutes from time Craney fired a difficult chance over the bar and, in the last minute, Dunbavin somehow managed to turn over a bullet header from Murphy right under his own crossbar.
It was left to Craney to have the last word as he was picked out by Whalley's precision pass before rifling the ball left-footed past Danby.