Two goals in five first half minutes had put the home side in control, but they had to survive late pressure after Jermaine Easter gave County hope of a draw with a late goal.
Before the kick-off a minute's silence was held to mark the deaths of George Best and Mansfield's goalkeeping coach Peter Wilson, who died a week earlier during the warm-up at Shrewsbury.
And the Stags, looking for a victory tribute to their coach, twice went close to a goal in the first minute during a storming start.
Two dangerous crosses from Adam Rundle and Gavin Peers created chaos inside the Stockport six-yard area. First Rundle's pass bounced narrowly wide off Jonathon D'Lareya and then Peers' deep cross was headed away from under his own bar by Michael Raynes.
In the 10th minute Peers' diving header from a Rundle corner brushed the outside of the post and then Richie Barker's dipping 25-yard volley was acrobatically tipped wide by the flying James Spencer as Mansfield maintained the pressure.
At the other end Keith Briggs' close range drive was deflected for a corner and then Easter's scuffed shot rolled agonisingly wide as County briefly threatened with three corners in a minute.
But it was Mansfield who continued to create the better chances.
Barker was denied by Spencer's brave save at his feet and then Giles Coke struck the bar with a deflected 20-yard drive.
However the Stags finally grabbed the goal they deserved in the 26th minute, Peers stooping to head in a Rundle free-kick.
Five minutes later Barker doubled the lead, collecting Steven Dawson's pass and rounding the keeper before sliding into an empty net.
Mansfield then wasted four chances to secure victory and County finally grabbed a lifeline in the 80th minute when substitute Michael Malcolm released Easter for a neat finish through the legs of Kevin Pressman.
However the Stags, who had thrown away a two-goal lead at Stockport on the opening day of the season, this time hung on for victory.