Gregory doubled the advantage just before half-time when he drove a low shot into the bottom corner.
Steve Daly's 18-yard strike into the top corner gave the home side hope but Mansfield held on for the win.
Southport: McMillan, Lee, Lever (Shaun Gray 10), Flynn (Williams 46), Davis, Winn, Blakeman (Barratt 72), Moogan, McGinn, McNeil, Daly.
Subs Not Used: Dickinson, Collins.
Booked: Moogan, McNeil.
Goals: Daly 80.
Mansfield: Marriott, Silk, Sandwith, Foster, Chris Smith, Istead, Mills, Nix, Medley (Duffy 83), Gregory (Cain 61), Connor. Subs Not Used: Collett, Naylor, Parker.
Booked: Connor.
Goals: Istead 18, Gregory 40.
Att: 1,289.
Ref: R West (England).
Source: BBC Sport
Source: BBC Sport