The match - finely poised at 1-1 - was transformed in the 66th minute when Mansfield striker Richie Barker was sent off.
Barker was dismissed for his second yellow card after Ben Davies appeared to over-react to the forward's challenge.
Just three minutes later Chester took full advantage as former Stags striker Derek Asamoah flicked in Davies' free-kick.
In a thrilling finish Mansfield substitute Adam Birchall rattled the bar, Giles Coke's injury time drive flew narrowly wide and Stephen Dawson's last gasp piledriver was tipped away for a corner as the home side searched for a leveller.
Freezing conditions made life difficult for the Stags class of 2006 against a side labelled the Stags class of 2005.
Curle had brought six players from Mansfield's team last season back to Field Mill as struggling City looked to end Mansfield's six-match unbeaten home run.
City should have taken the lead inside the first 60 seconds as Mansfield failed to clear a Davies free-kick and Asamoah's volley was turned away by Kevin Pressman.
A minute before the interval Ryan Lowe squandered the best chance of the first half by blazing wide of an empty net.
Sixty seconds into the second half Chester forced two goalline clearances at a corner with Barker and Alex Baptiste denying Asamoah and Stewart Drummond.
Those clearances proved vital six minutes later when Danny Reet gave the Stags the lead as he turned in an Adam Rundle cross.
But within two minutes Scott McNiven thumped Chester level with a 25-yard drive as the match finally came alive.
Barker's rising 20-yard drive almost restored Mansfield's lead 30 seconds later, while at the other end Asamoah poked wide from six yards.
But he made no mistake with the winner in the 69th minute to the delight of Curle.