The hosts dominated in the early stages but they could not find a way past Wrexham stopper Andy Coughlin until the 40th minute when Green scored from the spot after Louis Briscoe was brought down by Glen Little in the box.
Paul Cox's men pushed for a second after the re-start and it very nearly came in the 67th minute when Lee Stevenson let fly from the left side of the box, only for his effort to hit the bar and bounce away to safety.
Wrexham defender David Artell saw red in the 90th minute when he fouled Colin Daniel.
The Stags held on to win and they go up as Blue Square Bet Premier champions, ending a five-year exile from the Football League.
- Sports & Recreation
- Louis Briscoe
- Andy Coughlin