It ends a five-year stay back in the Football League after a two-year drop to the Conference in 2007.
Despite Mansfield having most of the first-half play and more of the chances, they found themselves 2-0 down and reduced to 10 men by half-time.
Oliver Palmer, John Dempster and Matt Rhead all failed to beat Martin Rice with good headed chances.
Dempster had inadvertently set the Gulls on their way as he put Baily Cargill’s left-wing cross past his own goalkeeper at the near post on 13 minutes.
It was 2-0 just after the half-hour mark as Courtney Cameron sent over a great cross from the left and, although keeper Lewis Price made a superb save to deny Ashley Yeoman from point-blank range, Yeoman beat him with the follow-up.
Stags’ task was made even harder on 44 minutes when Rhead was sent off for sliding in late and catching Dale Tonge with his studs.
But Stags pulled one back immediately after the break as James Jennings headed a Chris Clements corner goalwards with Damon Lathrope getting a touch on it but unable to prevent it going in.
On 61 minutes Price turned Cameron’s finish over the crossbar, after he had been sent through one-on-one.
Then Krystian Pearce wasted a golden chance as he fired over unchallenged from six yards from a corner.
But Shaquile Coulthirst sealed what proved to be a hollow win with a powerful close-range header from a Jordan Chapell cross from the right with 12 minutes left.