Curle was dismissed by the Stags last season but saw his new club get off to the best possible start with a goal inside two minutes when Gregg Blundell headed home at the far post.
Mansfield's best threat came on 26 minutes when a mis-hit shot by Giles Coke came the way of Richie Barker, who could only direct his header over the bar.
Ten minutes before the interval the home side should have doubled their advantage after veteran goalkeeper Kevin Pressman spilled the ball, presenting it to Blundell. But the striker's effort came back off the bar and Ben Davies was unable to capitalise on the rebound.
The visitors started the second half brightly and within a minute Coke forced Chris MacKenzie into an excellent save with a rasping low drive from distance.
At the other end Ryan Lowe was twice denied by excellent saves from Pressman.
Chester were well on top and it came as no surprise when they doubled their advantage on the hour mark as Michael Branch crossed to Blundell, who had the easy job of heading home from close range.
Mansfield hauled themselves back into the game seven minutes later when substitute Adam Rundle delivered a perfect cross for Alex Baptiste to power a header past MacKenzie.
Blundell then shot wide with a decent chance after the ball dropped invitingly to him 12 yards from goal.
However, any hopes the Stags had of getting something from the game were extinguished ten minutes from time, as a Branch cross was neatly laid off by Blundell and Lowe produced the necessary finish with an exquisite strike.