Hosts Leamington made life difficult for the Stags for much of the first half, but their resilience finally cracked during a second period of incessant pressure as Green fired home from 12 yards.
It was Leamington, who finished 7th in the Evo-Stik Southern Premier last season, who got off to the better start. Stags’ defender Ritchie Sutton, playing at centre half, had to be on guard to block a goalbound effort from Alex Taylor.
At the other end, Stags came to life largely thanks to Lindon Meikle. The winger set up a chance for Ben Hutchinson, followed up by a solo effort, but neither tested the home ‘keeper.
Leamington thought they had taken the lead during an evenly-matched first half - but the referee spotted a clear foul on goalkeeper Shane Redmond as the ball was floated into the box from a free kick.
Home goalkeeper Liam Vaughan had to get down low to keep out a well-struck effort from midfielder Jamie Tolley, before Stags upped the ante with a fresh starting 11 in the second period.
Stags ‘keeper Alan Marriott had to get behind a rasping strike from Sam Adkins, but after that it was all one-way traffic.
New signing Jamie Hand showed why Paul Cox had brought him to the club with a fine second half display which started with an assist to Green, who dragged his shot wide from a tight angle.
Chris Clements, another of Stags’ new faces, let fly on the volley with 15 minutes to go, but it was aimed straight at the home shot stopper.
Leamington were finally undone after Stags' dominance paid off on 82 minutes. Another classy pass over the top from Hand saw Green upended in the area and the sharp shooter made no mistake from the penalty mark as he powered it down the middle to get Stags off to a winning pre-season start.
First half: Redmond, Beevers, Sutton, Dempster, Sam Benjamin (trialist), Poku, Roberts, Hutchinson, Wright, Meikle, Briscoe
Second half: Marriott, Todd, Pilkington, Jones, Hand, Owens, Tolley, Clements, Stevenson, Green, Rhead